Abdelrahman Said
3778 lines
134 KiB
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3778 lines
134 KiB
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<div class="chapter">
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<div class="titlepage"><div><div><h1 class="title">
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<a name="igraph-Layout"></a>Chapter 29. Generating layouts for graph drawing</h1></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="igraph-Layout.html#two-d-layout-generators">1. 2D layout generators</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#layouts-for-trees-and-acyclic-graphs">2. Layouts for trees and acyclic graphs</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#three-d-layout-generators">3. 3D layout generators</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#pp-layouts">4. Post-processing layouts</a></span></dt>
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</dl></div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="two-d-layout-generators"></a>1. 2D layout generators</h2></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_random">1.1. <code class="function">igraph_layout_random</code> — Places the vertices uniformly randomly within a square.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_circle">1.2. <code class="function">igraph_layout_circle</code> — Places the vertices uniformly on a circle in arbitrary order.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_star">1.3. <code class="function">igraph_layout_star</code> — Generates a star-like layout.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_grid">1.4. <code class="function">igraph_layout_grid</code> — Places the vertices on a regular grid on the plane.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_graphopt">1.5. <code class="function">igraph_layout_graphopt</code> — Optimizes vertex layout via the graphopt algorithm.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_bipartite">1.6. <code class="function">igraph_layout_bipartite</code> — Simple layout for bipartite graphs.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#drl-layout-generator">1.7. The DrL layout generator</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_fruchterman_reingold">1.8. <code class="function">igraph_layout_fruchterman_reingold</code> — Places the vertices on a plane according to the Fruchterman-Reingold algorithm.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_kamada_kawai">1.9. <code class="function">igraph_layout_kamada_kawai</code> — Places the vertices on a plane according to the Kamada-Kawai algorithm.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_gem">1.10. <code class="function">igraph_layout_gem</code> — Layout graph according to GEM algorithm.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_davidson_harel">1.11. <code class="function">igraph_layout_davidson_harel</code> — Davidson-Harel layout algorithm.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_mds">1.12. <code class="function">igraph_layout_mds</code> — Place the vertices on a plane using multidimensional scaling.</a></span></dt>
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<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_lgl">1.13. <code class="function">igraph_layout_lgl</code> — Force based layout algorithm for large graphs.</a></span></dt>
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</dl></div>
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<p>Layout generator functions (or at least most of them) try to place the
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vertices and edges of a graph on a 2D plane or in 3D space in a way
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which visually pleases the human eye.</p>
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<p>They take a graph object and a number of parameters as arguments
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and return an <span class="type">igraph_matrix_t</span>, in which each row gives the
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coordinates of a vertex.</p>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="igraph_layout_random"></a>1.1. <code class="function">igraph_layout_random</code> — Places the vertices uniformly randomly within a square.</h3></div></div></div>
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<a class="indexterm" name="id-1.30.2.4.2"></a><p>
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</p>
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<div class="informalexample"><pre class="programlisting">
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igraph_error_t igraph_layout_random(const igraph_t *graph, igraph_matrix_t *res);
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</pre></div>
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<p>
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</p>
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<p>
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Vertex coordinates range from -1 to 1, and are placed in two columns
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of a matrix, with a row for each vertex.
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized graph object.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized matrix object. This will
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contain the result and will be resized as needed.
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</p></td>
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</tr>
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</tbody>
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</table></div>
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<p>
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</p>
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<p><b>Returns: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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Error code.
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</p></td>
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</tr></tbody>
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</table></div>
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<p>
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Time complexity: O(|V|), the number of vertices.
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</p>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="igraph_layout_circle"></a>1.2. <code class="function">igraph_layout_circle</code> — Places the vertices uniformly on a circle in arbitrary order.</h3></div></div></div>
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<a class="indexterm" name="id-1.30.2.5.2"></a><p>
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</p>
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<div class="informalexample"><pre class="programlisting">
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igraph_error_t igraph_layout_circle(const igraph_t *graph, igraph_matrix_t *res,
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igraph_vs_t order);
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</pre></div>
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<p>
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</p>
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<p>
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized graph object.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized matrix object. This will
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contain the result and will be resized as needed.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>order</code></em>:</span></p></td>
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<td><p>
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The order of the vertices on the circle. The vertices
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not included here, will be placed at (0,0). Supply
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<a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version)."><code class="function">igraph_vss_all()</code></a> here to place vertices in the
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order of their vertex IDs.
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</p></td>
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</tr>
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</tbody>
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</table></div>
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<p>
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</p>
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<p><b>Returns: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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Error code.
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</p></td>
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</tr></tbody>
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</table></div>
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<p>
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Time complexity: O(|V|), the number of vertices.
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</p>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="igraph_layout_star"></a>1.3. <code class="function">igraph_layout_star</code> — Generates a star-like layout.</h3></div></div></div>
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<a class="indexterm" name="id-1.30.2.6.2"></a><p>
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</p>
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<div class="informalexample"><pre class="programlisting">
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igraph_error_t igraph_layout_star(const igraph_t *graph, igraph_matrix_t *res,
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igraph_int_t center, const igraph_vector_int_t *order);
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</pre></div>
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<p>
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</p>
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<p>
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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The input graph. Its edges are ignored by this function.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized matrix object. This will
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contain the result and will be resized as needed.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>center</code></em>:</span></p></td>
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<td><p>
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The id of the vertex to put in the center. You can set it to
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any arbitrary value for the special case when the input graph has no
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vertices; otherwise it must be between 0 and the number of vertices
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minus 1.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>order</code></em>:</span></p></td>
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<td><p>
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A numeric vector giving the order of the vertices
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(including the center vertex!). If a null pointer, then the
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vertices are placed in increasing vertex ID order.
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</p></td>
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</tr>
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</tbody>
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</table></div>
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<p>
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</p>
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<p><b>Returns: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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Error code.
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</p></td>
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</tr></tbody>
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</table></div>
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<p>
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Time complexity: O(|V|), linear in the number of vertices.
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</p>
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<p><b>See also: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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<a class="link" href="igraph-Layout.html#igraph_layout_circle" title="1.2. igraph_layout_circle — Places the vertices uniformly on a circle in arbitrary order."><code class="function">igraph_layout_circle()</code></a> and other layout generators.
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</p></td>
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</tr></tbody>
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</table></div>
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<p>
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</p>
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||
</div>
|
||
<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="igraph_layout_grid"></a>1.4. <code class="function">igraph_layout_grid</code> — Places the vertices on a regular grid on the plane.</h3></div></div></div>
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<a class="indexterm" name="id-1.30.2.7.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_grid(const igraph_t *graph, igraph_matrix_t *res, igraph_int_t width);
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</pre></div>
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<p>
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</p>
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||
<p>
|
||
|
||
|
||
|
||
|
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</p>
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<p><b>Arguments: </b>
|
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</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
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<colgroup>
|
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<col align="left" valign="top">
|
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<col>
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||
</colgroup>
|
||
<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized graph object.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized matrix object. This will
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contain the result and will be resized as needed.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>width</code></em>:</span></p></td>
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<td><p>
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The number of vertices in a single row of the grid.
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When zero or negative, the width of the grid will be the
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square root of the number of vertices, rounded up if needed.
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</p></td>
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</tr>
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</tbody>
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</table></div>
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<p>
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</p>
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<p><b>Returns: </b></p>
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||
<div class="variablelist"><table border="0" class="variablelist">
|
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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Error code. The current implementation always returns with
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success.
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</p></td>
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</tr></tbody>
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</table></div>
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<p>
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Time complexity: O(|V|), the number of vertices.
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||
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||
</p>
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||
</div>
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<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_graphopt"></a>1.5. <code class="function">igraph_layout_graphopt</code> — Optimizes vertex layout via the graphopt algorithm.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.8.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_graphopt(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_int_t niter,
|
||
igraph_real_t node_charge, igraph_real_t node_mass,
|
||
igraph_real_t spring_length,
|
||
igraph_real_t spring_constant,
|
||
igraph_real_t max_sa_movement,
|
||
igraph_bool_t use_seed);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This is a port of the graphopt layout algorithm by Michael Schmuhl.
|
||
graphopt version 0.4.1 was rewritten in C, the support for
|
||
layers was removed and the code was reorganized to avoid some
|
||
unnecessary steps when the node charge (see below) is zero.
|
||
|
||
</p>
|
||
<p>
|
||
Graphopt uses physical analogies for defining attracting and repelling
|
||
forces among the vertices and then the physical system is simulated
|
||
until it reaches an equilibrium. (There is no simulated annealing or
|
||
anything like that, so a stable fixed point is not guaranteed.)
|
||
|
||
</p>
|
||
<p>
|
||
See also
|
||
<a class="ulink" href="https://web.archive.org/web/20220611030748/http://www.schmuhl.org/graphopt/" target="_top">https://web.archive.org/web/20220611030748/http://www.schmuhl.org/graphopt/</a>
|
||
and
|
||
<a class="ulink" href="https://sourceforge.net/projects/graphopt/" target="_top">https://sourceforge.net/projects/graphopt/</a>
|
||
for the original graphopt.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix, the result will be stored here
|
||
and its initial contents are used as the starting point of the simulation
|
||
if the <em class="parameter"><code>use_seed</code></em> argument is true. Note that in this case the
|
||
matrix should have the proper size, otherwise a warning is issued and
|
||
the supplied values are ignored. If no starting positions are given
|
||
(or they are invalid) then a random starting position is used.
|
||
The matrix will be resized if needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>niter</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer constant, the number of iterations to perform.
|
||
Should be a couple of hundred in general. If you have a large graph
|
||
then you might want to only do a few iterations and then check the
|
||
result. If it is not good enough you can feed it in again in
|
||
the <em class="parameter"><code>res</code></em> argument. The original graphopt default is 500.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>node_charge</code></em>:</span></p></td>
|
||
<td><p>
|
||
The charge of the vertices, used to calculate electric
|
||
repulsion. The original graphopt default is 0.001.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>node_mass</code></em>:</span></p></td>
|
||
<td><p>
|
||
The mass of the vertices, used for the spring forces.
|
||
The original graphopt defaults to 30.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>spring_length</code></em>:</span></p></td>
|
||
<td><p>
|
||
The length of the springs.
|
||
The original graphopt defaults to zero.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>spring_constant</code></em>:</span></p></td>
|
||
<td><p>
|
||
The spring constant, the original graphopt defaults
|
||
to one.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_sa_movement</code></em>:</span></p></td>
|
||
<td><p>
|
||
Real constant, it gives the maximum amount of movement
|
||
allowed in a single step along a single axis. The original graphopt
|
||
default is 5.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, whether to use the positions in <em class="parameter"><code>res</code></em> as
|
||
a starting configuration. See also <em class="parameter"><code>res</code></em> above.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(n (|V|^2+|E|) ), n is the number of iterations,
|
||
|V| is the number of vertices, |E| the number
|
||
of edges. If <em class="parameter"><code>node_charge</code></em> is zero then it is only O(n|E|).
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_bipartite"></a>1.6. <code class="function">igraph_layout_bipartite</code> — Simple layout for bipartite graphs.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.9.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_bipartite(const igraph_t *graph,
|
||
const igraph_vector_bool_t *types,
|
||
igraph_matrix_t *res, igraph_real_t hgap,
|
||
igraph_real_t vgap, igraph_int_t maxiter);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
The layout is created by first placing the vertices in two rows,
|
||
according to their types. Then the positions within the rows are
|
||
optimized to minimize edge crossings, by calling <a class="link" href="igraph-Layout.html#igraph_layout_sugiyama" title="2.4. igraph_layout_sugiyama — Sugiyama layout algorithm for layered directed acyclic graphs."><code class="function">igraph_layout_sugiyama()</code></a>.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
A boolean vector containing ones and zeros, the vertex
|
||
types. Its length must match the number of vertices in the graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix, the result, the x and
|
||
y coordinates are stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hgap</code></em>:</span></p></td>
|
||
<td><p>
|
||
The preferred minimum horizontal gap between vertices
|
||
in the same layer (i.e. vertices of the same type).
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>vgap</code></em>:</span></p></td>
|
||
<td><p>
|
||
The distance between layers.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxiter</code></em>:</span></p></td>
|
||
<td><p>
|
||
Maximum number of iterations in the crossing
|
||
minimization stage. 100 is a reasonable default; if you feel
|
||
that you have too many edge crossings, increase this.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_sugiyama" title="2.4. igraph_layout_sugiyama — Sugiyama layout algorithm for layered directed acyclic graphs."><code class="function">igraph_layout_sugiyama()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="drl-layout-generator"></a>1.7. The DrL layout generator</h3></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_drl_options_t">1.7.1. <code class="function">igraph_layout_drl_options_t</code> — Parameters for the DrL layout generator</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_drl_default_t">1.7.2. <code class="function">igraph_layout_drl_default_t</code> — Predefined parameter templates for the DrL layout generator</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_drl_options_init">1.7.3. <code class="function">igraph_layout_drl_options_init</code> — Initialize parameters for the DrL layout generator</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_drl">1.7.4. <code class="function">igraph_layout_drl</code> — The DrL layout generator</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_drl_3d">1.7.5. <code class="function">igraph_layout_drl_3d</code> — The DrL layout generator, 3d version.</a></span></dt>
|
||
</dl></div>
|
||
<p>
|
||
DrL is a sophisticated layout generator developed and implemented by
|
||
Shawn Martin et al. As of October 2012 the original DrL homepage is
|
||
unfortunately not available. You can read more about this algorithm
|
||
in the following technical report: Martin, S., Brown, W.M.,
|
||
Klavans, R., Boyack, K.W., DrL: Distributed Recursive (Graph)
|
||
Layout. SAND Reports, 2008. 2936: p. 1-10.
|
||
</p>
|
||
<p>
|
||
Only a subset of the complete DrL functionality is
|
||
included in igraph, parallel runs and recursive, multi-level
|
||
layouting is not supported.
|
||
</p>
|
||
<p>
|
||
The parameters of the layout are stored in an <a class="link" href="igraph-Layout.html#igraph_layout_drl_options_t" title="1.7.1. igraph_layout_drl_options_t — Parameters for the DrL layout generator"><code class="function">igraph_layout_drl_options_t</code></a> structure, this can be initialized by
|
||
calling the function <a class="link" href="igraph-Layout.html#igraph_layout_drl_options_init" title="1.7.3. igraph_layout_drl_options_init — Initialize parameters for the DrL layout generator"><code class="function">igraph_layout_drl_options_init()</code></a>.
|
||
The fields of this structure can then be adjusted by hand if needed.
|
||
The layout is calculated by an <a class="link" href="igraph-Layout.html#igraph_layout_drl" title="1.7.4. igraph_layout_drl — The DrL layout generator"><code class="function">igraph_layout_drl()</code></a> call.
|
||
</p>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="igraph_layout_drl_options_t"></a>1.7.1. <code class="function">igraph_layout_drl_options_t</code> — Parameters for the DrL layout generator</h4></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.10.5.2"></a><p>
|
||
</p>
|
||
<pre class="programlisting">
|
||
typedef struct igraph_layout_drl_options_t {
|
||
igraph_real_t edge_cut;
|
||
igraph_int_t init_iterations;
|
||
igraph_real_t init_temperature;
|
||
igraph_real_t init_attraction;
|
||
igraph_real_t init_damping_mult;
|
||
igraph_int_t liquid_iterations;
|
||
igraph_real_t liquid_temperature;
|
||
igraph_real_t liquid_attraction;
|
||
igraph_real_t liquid_damping_mult;
|
||
igraph_int_t expansion_iterations;
|
||
igraph_real_t expansion_temperature;
|
||
igraph_real_t expansion_attraction;
|
||
igraph_real_t expansion_damping_mult;
|
||
igraph_int_t cooldown_iterations;
|
||
igraph_real_t cooldown_temperature;
|
||
igraph_real_t cooldown_attraction;
|
||
igraph_real_t cooldown_damping_mult;
|
||
igraph_int_t crunch_iterations;
|
||
igraph_real_t crunch_temperature;
|
||
igraph_real_t crunch_attraction;
|
||
igraph_real_t crunch_damping_mult;
|
||
igraph_int_t simmer_iterations;
|
||
igraph_real_t simmer_temperature;
|
||
igraph_real_t simmer_attraction;
|
||
igraph_real_t simmer_damping_mult;
|
||
} igraph_layout_drl_options_t;
|
||
</pre>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
</p>
|
||
<p></p>
|
||
<p><b>Values: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">edge_cut</code>:</span></p></td>
|
||
<td><p>
|
||
The edge cutting parameter.
|
||
Edge cutting is done in the late stages of the
|
||
algorithm in order to achieve less dense layouts. Edges are cut
|
||
if there is a lot of stress on them (a large value in the
|
||
objective function sum). The edge cutting parameter is a value
|
||
between 0 and 1 with 0 representing no edge cutting and 1
|
||
representing maximal edge cutting. The default value is 32/40.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">init_iterations</code>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations, initial phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">init_temperature</code>:</span></p></td>
|
||
<td><p>
|
||
Start temperature, initial phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">init_attraction</code>:</span></p></td>
|
||
<td><p>
|
||
Attraction, initial phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">init_damping_mult</code>:</span></p></td>
|
||
<td><p>
|
||
Damping factor, initial phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">liquid_iterations</code>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations in the liquid phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">liquid_temperature</code>:</span></p></td>
|
||
<td><p>
|
||
Start temperature in the liquid phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">liquid_attraction</code>:</span></p></td>
|
||
<td><p>
|
||
Attraction in the liquid phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">liquid_damping_mult</code>:</span></p></td>
|
||
<td><p>
|
||
Multiplicatie damping factor, liquid phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">expansion_iterations</code>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations in the expansion phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">expansion_temperature</code>:</span></p></td>
|
||
<td><p>
|
||
Start temperature in the expansion phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">expansion_attraction</code>:</span></p></td>
|
||
<td><p>
|
||
Attraction, expansion phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">expansion_damping_mult</code>:</span></p></td>
|
||
<td><p>
|
||
Damping factor, expansion phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">cooldown_iterations</code>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations in the cooldown phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">cooldown_temperature</code>:</span></p></td>
|
||
<td><p>
|
||
Start temperature in the cooldown phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">cooldown_attraction</code>:</span></p></td>
|
||
<td><p>
|
||
Attraction in the cooldown phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">cooldown_damping_mult</code>:</span></p></td>
|
||
<td><p>
|
||
Damping fact int the cooldown phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">crunch_iterations</code>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations in the crunch phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">crunch_temperature</code>:</span></p></td>
|
||
<td><p>
|
||
Start temperature in the crunch phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">crunch_attraction</code>:</span></p></td>
|
||
<td><p>
|
||
Attraction in the crunch phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">crunch_damping_mult</code>:</span></p></td>
|
||
<td><p>
|
||
Damping factor in the crunch phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">simmer_iterations</code>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations in the simmer phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">simmer_temperature</code>:</span></p></td>
|
||
<td><p>
|
||
Start temperature in te simmer phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">simmer_attraction</code>:</span></p></td>
|
||
<td><p>
|
||
Attraction in the simmer phase.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">simmer_damping_mult</code>:</span></p></td>
|
||
<td><p>
|
||
Multiplicative damping factor in the simmer phase.</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="igraph_layout_drl_default_t"></a>1.7.2. <code class="function">igraph_layout_drl_default_t</code> — Predefined parameter templates for the DrL layout generator</h4></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.10.6.2"></a><p>
|
||
</p>
|
||
<pre class="programlisting">
|
||
typedef enum { IGRAPH_LAYOUT_DRL_DEFAULT = 0,
|
||
IGRAPH_LAYOUT_DRL_COARSEN,
|
||
IGRAPH_LAYOUT_DRL_COARSEST,
|
||
IGRAPH_LAYOUT_DRL_REFINE,
|
||
IGRAPH_LAYOUT_DRL_FINAL
|
||
} igraph_layout_drl_default_t;
|
||
</pre>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
These constants can be used to initialize a set of DrL parameters.
|
||
These can then be modified according to the user's needs.
|
||
</p>
|
||
<p><b>Values: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_LAYOUT_DRL_DEFAULT</code>:</span></p></td>
|
||
<td><p>
|
||
The deafult parameters.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_LAYOUT_DRL_COARSEN</code>:</span></p></td>
|
||
<td><p>
|
||
Slightly modified parameters to
|
||
get a coarser layout.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_LAYOUT_DRL_COARSEST</code>:</span></p></td>
|
||
<td><p>
|
||
An even coarser layout.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_LAYOUT_DRL_REFINE</code>:</span></p></td>
|
||
<td><p>
|
||
Refine an already calculated layout.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_LAYOUT_DRL_FINAL</code>:</span></p></td>
|
||
<td><p>
|
||
Finalize an already refined layout.</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="igraph_layout_drl_options_init"></a>1.7.3. <code class="function">igraph_layout_drl_options_init</code> — Initialize parameters for the DrL layout generator</h4></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.10.7.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_drl_options_init(igraph_layout_drl_options_t *options,
|
||
igraph_layout_drl_default_t templ);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function can be used to initialize the struct holding the
|
||
parameters for the DrL layout generator. There are a number of
|
||
predefined templates available, it is a good idea to start from one
|
||
of these by modifying some parameters.
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>options</code></em>:</span></p></td>
|
||
<td><p>
|
||
The struct to initialize.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>templ</code></em>:</span></p></td>
|
||
<td><p>
|
||
The template to use. Currently the following templates
|
||
are supplied: <code class="constant">IGRAPH_LAYOUT_DRL_DEFAULT</code>, <code class="constant">IGRAPH_LAYOUT_DRL_COARSEN</code>, <code class="constant">IGRAPH_LAYOUT_DRL_COARSEST</code>,
|
||
<code class="constant">IGRAPH_LAYOUT_DRL_REFINE</code> and <code class="constant">IGRAPH_LAYOUT_DRL_FINAL</code>.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(1).
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="igraph_layout_drl"></a>1.7.4. <code class="function">igraph_layout_drl</code> — The DrL layout generator</h4></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.10.8.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_drl(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_bool_t use_seed,
|
||
const igraph_layout_drl_options_t *options,
|
||
const igraph_vector_t *weights);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function implements the force-directed DrL layout generator.
|
||
Please see more in the following technical report: Martin, S.,
|
||
Brown, W.M., Klavans, R., Boyack, K.W., DrL: Distributed Recursive
|
||
(Graph) Layout. SAND Reports, 2008. 2936: p. 1-10.
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, if true, then the coordinates
|
||
supplied in the <em class="parameter"><code>res</code></em> argument are used as starting points.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a matrix, the result layout is stored
|
||
here. It will be resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>options</code></em>:</span></p></td>
|
||
<td><p>
|
||
The parameters to pass to the layout generator.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Edge weights, pointer to a vector. If this is a null
|
||
pointer then every edge will have the same weight.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: ???.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h4 class="title">
|
||
<a name="igraph_layout_drl_3d"></a>1.7.5. <code class="function">igraph_layout_drl_3d</code> — The DrL layout generator, 3d version.</h4></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.10.9.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_drl_3d(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_bool_t use_seed,
|
||
const igraph_layout_drl_options_t *options,
|
||
const igraph_vector_t *weights);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function implements the force-directed DrL layout generator.
|
||
Please see more in the technical report: Martin, S., Brown, W.M.,
|
||
Klavans, R., Boyack, K.W., DrL: Distributed Recursive (Graph)
|
||
Layout. SAND Reports, 2008. 2936: p. 1-10.
|
||
|
||
</p>
|
||
<p> This function uses a modified DrL generator that does
|
||
the layout in three dimensions.
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, if true, then the coordinates
|
||
supplied in the <em class="parameter"><code>res</code></em> argument are used as starting points.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a matrix, the result layout is stored
|
||
here. It will be resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>options</code></em>:</span></p></td>
|
||
<td><p>
|
||
The parameters to pass to the layout generator.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Edge weights, pointer to a vector. If this is a null
|
||
pointer then every edge will have the same weight.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: ???.
|
||
|
||
</p>
|
||
<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_drl" title="1.7.4. igraph_layout_drl — The DrL layout generator"><code class="function">igraph_layout_drl()</code></a> for the standard 2d version.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_fruchterman_reingold"></a>1.8. <code class="function">igraph_layout_fruchterman_reingold</code> — Places the vertices on a plane according to the Fruchterman-Reingold algorithm.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.11.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_fruchterman_reingold(const igraph_t *graph,
|
||
igraph_matrix_t *res,
|
||
igraph_bool_t use_seed,
|
||
igraph_int_t niter,
|
||
igraph_real_t start_temp,
|
||
igraph_layout_grid_t grid,
|
||
const igraph_vector_t *weights,
|
||
const igraph_vector_t *minx,
|
||
const igraph_vector_t *maxx,
|
||
const igraph_vector_t *miny,
|
||
const igraph_vector_t *maxy);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
This is a force-directed layout that simulates an attractive force <code class="constant">f_a</code> between
|
||
connected vertex pairs and a repulsive force <code class="constant">f_r</code> between all vertex pairs.
|
||
The forces are computed as a function of the distance <code class="constant">d</code> between the two vertices as
|
||
|
||
</p>
|
||
<p>
|
||
<code class="literal">f_a(d) = -w * d^2</code> and <code class="literal">f_r(d) = 1/d</code>,
|
||
|
||
</p>
|
||
<p>
|
||
where <code class="constant">w</code> represents the edge weight. The equilibrium distance of two connected
|
||
vertices is thus <code class="literal">1/w^3</code>, assuming no other forces acting on them.
|
||
|
||
</p>
|
||
<p>
|
||
In disconnected graphs, igraph effectively inserts a weak connection of weight
|
||
<code class="literal">n^(-3/2)</code> between all pairs of vertices, where <code class="constant">n</code> is the vertex count.
|
||
This ensures that components are kept near each other.
|
||
|
||
</p>
|
||
<p>
|
||
Reference:
|
||
|
||
</p>
|
||
<p>
|
||
Fruchterman, T.M.J. and Reingold, E.M.:
|
||
Graph Drawing by Force-directed Placement.
|
||
Software -- Practice and Experience, 21/11, 1129--1164,
|
||
1991. <a class="ulink" href="https://doi.org/10.1002/spe.4380211102" target="_top">https://doi.org/10.1002/spe.4380211102</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will
|
||
contain the result and will be resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
If true the supplied values in the
|
||
<em class="parameter"><code>res</code></em> argument are used as an initial layout, if
|
||
false a random initial layout is used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>niter</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of iterations to do. A reasonable
|
||
default value is 500.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>start_temp</code></em>:</span></p></td>
|
||
<td><p>
|
||
Start temperature. This is the maximum amount
|
||
of movement allowed along one axis, within one step, for a
|
||
vertex. Currently it is decreased linearly to zero during
|
||
the iteration.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>grid</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to use the (fast but less accurate) grid based
|
||
version of the algorithm. Possible values: <code class="constant">IGRAPH_LAYOUT_GRID</code>, <code class="constant">IGRAPH_LAYOUT_NOGRID</code>, <code class="constant">IGRAPH_LAYOUT_AUTOGRID</code>. The last one uses the grid based
|
||
version only for large graphs, currently the ones with
|
||
more than 1000 vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector containing edge weights. Weights must
|
||
be positive. If <code class="constant">NULL</code>, all edges are assumed to have weight 1.
|
||
The attraction along the edges will be multiplied by the weights,
|
||
resulting in vertices connected by a high-weight edge being placed
|
||
closer together.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>minx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">x</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>minx</code></em>, but the maximum <span class="quote">“<span class="quote">x</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>miny</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">y</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxy</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>miny</code></em>, but the maximum <span class="quote">“<span class="quote">y</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|^2) in each
|
||
iteration, |V| is the number of
|
||
vertices in the graph.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_kamada_kawai"></a>1.9. <code class="function">igraph_layout_kamada_kawai</code> — Places the vertices on a plane according to the Kamada-Kawai algorithm.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.12.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_kamada_kawai(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_bool_t use_seed, igraph_int_t maxiter,
|
||
igraph_real_t epsilon, igraph_real_t kkconst,
|
||
const igraph_vector_t *weights,
|
||
const igraph_vector_t *minx, const igraph_vector_t *maxx,
|
||
const igraph_vector_t *miny, const igraph_vector_t *maxy);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
This is a force-directed layout. A spring is inserted between all pairs
|
||
of vertices, both those which are directly connected and those that are not.
|
||
The unstretched length of springs is chosen based on the undirected graph distance
|
||
between the corresponding pair of vertices. Thus, in a weighted graph, increasing
|
||
the weight between two vertices pushes them apart. The Young modulus of springs
|
||
is inversely proportional to the graph distance, ensuring that springs between
|
||
far-apart veritces will have a smaller effect on the layout.
|
||
|
||
</p>
|
||
<p>
|
||
Disconnected graphs are handled by assuming that the graph distance between
|
||
vertices in different components is the same as the graph diameter.
|
||
|
||
</p>
|
||
<p>
|
||
This layout works particularly well for locally connected spatial networks
|
||
such as lattices.
|
||
|
||
</p>
|
||
<p>
|
||
This layout algorithm is not suitable for large graphs. The memory
|
||
requirements are of the order O(|V|^2).
|
||
|
||
</p>
|
||
<p>
|
||
Reference:
|
||
|
||
</p>
|
||
<p>
|
||
Kamada, T. and Kawai, S.:
|
||
An Algorithm for Drawing General Undirected Graphs.
|
||
Information Processing Letters, 31/1, 7--15, 1989.
|
||
<a class="ulink" href="https://doi.org/10.1016/0020-0190(89)90102-6" target="_top">https://doi.org/10.1016/0020-0190(89)90102-6</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
A graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will
|
||
contain the result (x-positions in column zero and
|
||
y-positions in column one) and will be resized if needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, whether to use the values supplied in the
|
||
<em class="parameter"><code>res</code></em> argument as the initial configuration. If zero and there
|
||
are any limits on the X or Y coordinates, then a random initial
|
||
configuration is used. Otherwise the vertices are placed on a
|
||
circle of radius 1 as the initial configuration.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxiter</code></em>:</span></p></td>
|
||
<td><p>
|
||
The maximum number of iterations to perform. A reasonable
|
||
default value is at least ten (or more) times the number of
|
||
vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>epsilon</code></em>:</span></p></td>
|
||
<td><p>
|
||
Stop the iteration, if the maximum delta value of the
|
||
algorithm is smaller than this. It is safe to leave it at zero,
|
||
and then <em class="parameter"><code>maxiter</code></em> iterations are performed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>kkconst</code></em>:</span></p></td>
|
||
<td><p>
|
||
The Kamada-Kawai vertex attraction constant.
|
||
Typical value: number of vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
A vector of edge weights. Weights are interpreted as edge
|
||
<span class="emphasis"><em>lengths</em></span> in the shortest path calculation used by the
|
||
Kamada-Kawai algorithm. Therefore, vertices connected by high-weight
|
||
edges will be placed further apart. Pass <code class="constant">NULL</code> to assume unit weights
|
||
for all edges.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>minx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">x</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>minx</code></em>, but the maximum <span class="quote">“<span class="quote">x</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>miny</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">y</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxy</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>miny</code></em>, but the maximum <span class="quote">“<span class="quote">y</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|) for each iteration, after an O(|V|^2
|
||
log|V|) initialization step. |V| is the number of vertices in the
|
||
graph.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_gem"></a>1.10. <code class="function">igraph_layout_gem</code> — Layout graph according to GEM algorithm.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.13.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_gem(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_bool_t use_seed, igraph_int_t maxiter,
|
||
igraph_real_t temp_max, igraph_real_t temp_min,
|
||
igraph_real_t temp_init);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
The GEM layout algorithm, as described in Arne Frick, Andreas Ludwig,
|
||
Heiko Mehldau: A Fast Adaptive Layout Algorithm for Undirected Graphs,
|
||
Proc. Graph Drawing 1994, LNCS 894, pp. 388-403, 1995.
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph. Edge directions are ignored in
|
||
directed graphs.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
The result is stored here. If the <em class="parameter"><code>use_seed</code></em> argument
|
||
is true, then this matrix is also used as the
|
||
starting point of the algorithm.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, whether to use the supplied coordinates in
|
||
<em class="parameter"><code>res</code></em> as the starting point. If false (zero), then a
|
||
uniform random starting point is used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxiter</code></em>:</span></p></td>
|
||
<td><p>
|
||
The maximum number of iterations to
|
||
perform. Updating a single vertex counts as an iteration.
|
||
A reasonable default is 40 * n * n, where n is the number of
|
||
vertices. The original paper suggests 4 * n * n, but this
|
||
usually only works if the other parameters are set up carefully.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>temp_max</code></em>:</span></p></td>
|
||
<td><p>
|
||
The maximum allowed local temperature. A reasonable
|
||
default is the number of vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>temp_min</code></em>:</span></p></td>
|
||
<td><p>
|
||
The global temperature at which the algorithm
|
||
terminates (even before reaching <em class="parameter"><code>maxiter</code></em> iterations). A
|
||
reasonable default is 1/10.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>temp_init</code></em>:</span></p></td>
|
||
<td><p>
|
||
Initial local temperature of all vertices. A
|
||
reasonable default is the square root of the number of
|
||
vertices.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(t * n * (n+e)), where n is the number of vertices,
|
||
e is the number of edges and t is the number of time steps
|
||
performed.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_davidson_harel"></a>1.11. <code class="function">igraph_layout_davidson_harel</code> — Davidson-Harel layout algorithm.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.14.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_davidson_harel(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_bool_t use_seed, igraph_int_t maxiter,
|
||
igraph_int_t fineiter, igraph_real_t cool_fact,
|
||
igraph_real_t weight_node_dist, igraph_real_t weight_border,
|
||
igraph_real_t weight_edge_lengths,
|
||
igraph_real_t weight_edge_crossings,
|
||
igraph_real_t weight_node_edge_dist);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function implements the algorithm by Davidson and Harel,
|
||
see Ron Davidson, David Harel: Drawing Graphs Nicely Using
|
||
Simulated Annealing. ACM Transactions on Graphics 15(4),
|
||
pp. 301-331, 1996.
|
||
<a class="ulink" href="https://doi.org/10.1145/234535.234538" target="_top">https://doi.org/10.1145/234535.234538</a>
|
||
|
||
</p>
|
||
<p>
|
||
The algorithm uses simulated annealing and a sophisticated
|
||
energy function, which is unfortunately hard to parameterize
|
||
for different graphs. The original publication did not disclose any
|
||
parameter values, and the ones below were determined by
|
||
experimentation.
|
||
|
||
</p>
|
||
<p>
|
||
The algorithm consists of two phases, an annealing phase, and a
|
||
fine-tuning phase. There is no simulated annealing in the second
|
||
phase.
|
||
|
||
</p>
|
||
<p>
|
||
Our implementation tries to follow the original publication, as
|
||
much as possible. The only major difference is that coordinates are
|
||
explicitly kept within the bounds of the rectangle of the layout.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph, edge directions are ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
A matrix, the result is stored here. It can be used to
|
||
supply start coordinates, see <em class="parameter"><code>use_seed</code></em>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, whether to use the supplied <em class="parameter"><code>res</code></em> as
|
||
start coordinates.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxiter</code></em>:</span></p></td>
|
||
<td><p>
|
||
The maximum number of annealing iterations. A
|
||
reasonable value for smaller graphs is 10.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>fineiter</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of fine tuning iterations. A reasonable
|
||
value is <code class="literal">max(10, log2(n))</code> where <code class="constant">n</code> is the
|
||
number of vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>cool_fact</code></em>:</span></p></td>
|
||
<td><p>
|
||
Cooling factor. A reasonable value is 0.75.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weight_node_dist</code></em>:</span></p></td>
|
||
<td><p>
|
||
Weight for the node-node distances
|
||
component of the energy function. Reasonable value: 1.0.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weight_border</code></em>:</span></p></td>
|
||
<td><p>
|
||
Weight for the distance from the border
|
||
component of the energy function. It can be set to zero, if
|
||
vertices are allowed to sit on the border.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weight_edge_lengths</code></em>:</span></p></td>
|
||
<td><p>
|
||
Weight for the edge length component
|
||
of the energy function, a reasonable value is the density of
|
||
the graph divided by 10.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weight_edge_crossings</code></em>:</span></p></td>
|
||
<td><p>
|
||
Weight for the edge crossing component
|
||
of the energy function, a reasonable default is 1 minus the
|
||
square root of the density of the graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weight_node_edge_dist</code></em>:</span></p></td>
|
||
<td><p>
|
||
Weight for the node-edge distance
|
||
component of the energy function. A reasonable value is
|
||
1 minus the density, divided by 5.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: one first phase iteration has time complexity
|
||
O(n^2+m^2), one fine tuning iteration has time complexity O(mn).
|
||
Time complexity might be smaller if some of the weights of the
|
||
components of the energy function are set to zero.
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_mds"></a>1.12. <code class="function">igraph_layout_mds</code> — Place the vertices on a plane using multidimensional scaling.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.15.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_mds(const igraph_t *graph, igraph_matrix_t *res,
|
||
const igraph_matrix_t *dist, igraph_int_t dim);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This layout requires a distance matrix, where the intersection of
|
||
row i and column j specifies the desired distance between vertex i
|
||
and vertex j. The algorithm will try to place the vertices in a
|
||
space having a given number of dimensions in a way that approximates
|
||
the distance relations prescribed in the distance matrix. igraph
|
||
uses the classical multidimensional scaling by Torgerson; for more
|
||
details, see Cox & Cox: Multidimensional Scaling (1994), Chapman
|
||
and Hall, London.
|
||
|
||
</p>
|
||
<p>
|
||
If the input graph is disconnected, igraph will decompose it
|
||
first into its subgraphs, lay out the subgraphs one by one
|
||
using the appropriate submatrices of the distance matrix, and
|
||
then merge the layouts using <a class="link" href="igraph-Layout.html#igraph_layout_merge_dla" title="4.1. igraph_layout_merge_dla — Merges multiple layouts by using a DLA algorithm."><code class="function">igraph_layout_merge_dla()</code></a>.
|
||
Since <a class="link" href="igraph-Layout.html#igraph_layout_merge_dla" title="4.1. igraph_layout_merge_dla — Merges multiple layouts by using a DLA algorithm."><code class="function">igraph_layout_merge_dla()</code></a> works for 2D layouts only,
|
||
you cannot run the MDS layout on disconnected graphs for
|
||
more than two dimensions.
|
||
|
||
</p>
|
||
<p>
|
||
Warning: if the graph is symmetric to the exchange of two vertices
|
||
(as is the case with leaves of a tree connecting to the same parent),
|
||
classical multidimensional scaling may assign the same coordinates to
|
||
these vertices.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
A graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will
|
||
contain the result and will be resized if needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>dist</code></em>:</span></p></td>
|
||
<td><p>
|
||
The distance matrix. It must be symmetric and this
|
||
function does not check whether the matrix is indeed
|
||
symmetric. Results are unspecified if you pass a non-symmetric
|
||
matrix here. You can set this parameter to null; in this
|
||
case, the undirected shortest path lengths between vertices
|
||
will be used as distances.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>dim</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of dimensions in the embedding space. For
|
||
2D layouts, supply 2 here.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Added in version 0.6.
|
||
|
||
</p>
|
||
<p>
|
||
Time complexity: usually around O(|V|^2 dim).
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_lgl"></a>1.13. <code class="function">igraph_layout_lgl</code> — Force based layout algorithm for large graphs.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.2.16.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_lgl(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_int_t maxit, igraph_real_t maxdelta,
|
||
igraph_real_t area, igraph_real_t coolexp,
|
||
igraph_real_t repulserad, igraph_real_t cellsize,
|
||
igraph_int_t proot);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
This is a layout generator similar to the Large Graph Layout
|
||
algorithm and program (<a class="ulink" href="http://lgl.sourceforge.net/" target="_top">http://lgl.sourceforge.net/</a>). But unlike LGL, this
|
||
version uses a Fruchterman-Reingold style simulated annealing
|
||
algorithm for placing the vertices. The speedup is achieved by
|
||
placing the vertices on a grid and calculating the repulsion only
|
||
for vertices which are closer to each other than a limit.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The (initialized) graph object to place. It must be connnected;
|
||
disconnected graphs are not handled by the algorithm.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object to hold the
|
||
result. It will be resized if needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxit</code></em>:</span></p></td>
|
||
<td><p>
|
||
The maximum number of cooling iterations to perform
|
||
for each layout step. A reasonable default is 150.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxdelta</code></em>:</span></p></td>
|
||
<td><p>
|
||
The maximum length of the move allowed for a vertex
|
||
in a single iteration. A reasonable default is the number of
|
||
vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>area</code></em>:</span></p></td>
|
||
<td><p>
|
||
This parameter gives the area of the square on which
|
||
the vertices will be placed. A reasonable default value is the
|
||
number of vertices squared.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>coolexp</code></em>:</span></p></td>
|
||
<td><p>
|
||
The cooling exponent. A reasonable default value is
|
||
1.5.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>repulserad</code></em>:</span></p></td>
|
||
<td><p>
|
||
Determines the radius at which vertex-vertex
|
||
repulsion cancels out attraction of adjacent vertices. A
|
||
reasonable default value is <em class="parameter"><code>area</code></em> times the number of vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>cellsize</code></em>:</span></p></td>
|
||
<td><p>
|
||
The size of the grid cells, one side of the
|
||
square. A reasonable default value is the fourth root of
|
||
<em class="parameter"><code>area</code></em> (or the square root of the number of vertices if <em class="parameter"><code>area</code></em>
|
||
is also left at its default value).
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>proot</code></em>:</span></p></td>
|
||
<td><p>
|
||
The root vertex, this is placed first, its neighbors
|
||
in the first iteration, second neighbors in the second, etc. If
|
||
negative then a random vertex is chosen.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Added in version 0.2.</p>
|
||
<p>
|
||
|
||
Time complexity: ideally O(dia*maxit*(|V|+|E|)), |V| is the number
|
||
of vertices,
|
||
dia is the diameter of the graph, worst case complexity is still
|
||
O(dia*maxit*(|V|^2+|E|)), this is the case when all vertices happen to be
|
||
in the same grid cell.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="layouts-for-trees-and-acyclic-graphs"></a>2. Layouts for trees and acyclic graphs</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_reingold_tilford">2.1. <code class="function">igraph_layout_reingold_tilford</code> — Reingold-Tilford layout for tree graphs.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_reingold_tilford_circular">2.2. <code class="function">igraph_layout_reingold_tilford_circular</code> — Circular Reingold-Tilford layout for trees.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_roots_for_tree_layout">2.3. <code class="function">igraph_roots_for_tree_layout</code> — Roots suitable for a nice tree layout.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_sugiyama">2.4. <code class="function">igraph_layout_sugiyama</code> — Sugiyama layout algorithm for layered directed acyclic graphs.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_umap">2.5. <code class="function">igraph_layout_umap</code> — Layout using Uniform Manifold Approximation and Projection (UMAP).</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_umap_compute_weights">2.6. <code class="function">igraph_layout_umap_compute_weights</code> — Compute weights for a UMAP layout starting from distances.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_reingold_tilford"></a>2.1. <code class="function">igraph_layout_reingold_tilford</code> — Reingold-Tilford layout for tree graphs.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.3.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_reingold_tilford(const igraph_t *graph,
|
||
igraph_matrix_t *res,
|
||
igraph_neimode_t mode,
|
||
const igraph_vector_int_t *roots,
|
||
const igraph_vector_int_t *rootlevel);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
Arranges the nodes in a tree where the given node is used as the root.
|
||
The tree is directed downwards and the parents are centered above its
|
||
children. For the exact algorithm, see:
|
||
|
||
</p>
|
||
<p>
|
||
Reingold, E and Tilford, J: Tidier drawing of trees.
|
||
IEEE Trans. Softw. Eng., SE-7(2):223--228, 1981.
|
||
<a class="ulink" href="https://doi.org/10.1109/TSE.1981.234519" target="_top">https://doi.org/10.1109/TSE.1981.234519</a>
|
||
|
||
</p>
|
||
<p>
|
||
If the given graph is not a tree, a breadth-first search is executed
|
||
first to obtain a possible spanning tree.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
The result, the coordinates in a matrix. The parameter
|
||
should point to an initialized matrix object and will be resized.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies which edges to consider when building the tree.
|
||
If it is <code class="constant">IGRAPH_OUT</code> then only the outgoing, if it is <code class="constant">IGRAPH_IN</code>
|
||
then only the incoming edges of a parent are considered. If it is
|
||
<code class="constant">IGRAPH_ALL</code> then all edges are used (this was the behavior in
|
||
igraph 0.5 and before). This parameter also influences how the root
|
||
vertices are calculated, if they are not given. See the <em class="parameter"><code>roots</code></em> parameter.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>roots</code></em>:</span></p></td>
|
||
<td><p>
|
||
The index of the root vertex or root vertices. The set of roots
|
||
should be specified so that all vertices of the graph are reachable from them.
|
||
Simply put, in the undirected case, one root should be given from each
|
||
connected component. If <em class="parameter"><code>roots</code></em> is <code class="constant">NULL</code> or a pointer to an empty vector,
|
||
then the roots will be selected automatically. Currently, automatic root
|
||
selection prefers low eccentricity vertices in graphs with fewer than
|
||
500 vertices, and high degree vertices (according to <em class="parameter"><code>mode</code></em>) in larger graphs.
|
||
The root selection heuristic may change without notice. To ensure a consistent
|
||
output, please specify the roots manually. The <a class="link" href="igraph-Layout.html#igraph_roots_for_tree_layout" title="2.3. igraph_roots_for_tree_layout — Roots suitable for a nice tree layout."><code class="function">igraph_roots_for_tree_layout()</code></a>
|
||
function gives more control over automatic root selection.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>rootlevel</code></em>:</span></p></td>
|
||
<td><p>
|
||
This argument can be useful when drawing forests which are
|
||
not trees (i.e. they are unconnected and have tree components). It specifies
|
||
the level of the root vertices for every tree in the forest. It is only
|
||
considered if not a null pointer and the <em class="parameter"><code>roots</code></em> argument is also given
|
||
(and it is not a null pointer of an empty vector).
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Added in version 0.2.
|
||
|
||
</p>
|
||
<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_reingold_tilford_circular" title="2.2. igraph_layout_reingold_tilford_circular — Circular Reingold-Tilford layout for trees."><code class="function">igraph_layout_reingold_tilford_circular()</code></a>, <a class="link" href="igraph-Layout.html#igraph_roots_for_tree_layout" title="2.3. igraph_roots_for_tree_layout — Roots suitable for a nice tree layout."><code class="function">igraph_roots_for_tree_layout()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
<div class="hideshow" onClick="toggle(this, event)">
|
||
<div class="example">
|
||
<a name="id-1.30.3.2.13.1"></a><p class="title"><b>Example 29.1. File <code class="code">examples/simple/igraph_layout_reingold_tilford.c</code></b></p>
|
||
<div class="example-contents">
|
||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||
<span class="strong"><strong>#include</strong></span> <math.h>
|
||
|
||
int <span class="strong"><strong>main</strong></span>(void) {
|
||
igraph_t g;
|
||
FILE *f;
|
||
igraph_matrix_t coords;
|
||
|
||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||
|
||
f = <span class="strong"><strong>fopen</strong></span>("igraph_layout_reingold_tilford.in", "r");
|
||
<span class="strong"><strong><a class="link" href="igraph-Foreign.html#igraph_read_graph_edgelist" title="1.1. igraph_read_graph_edgelist — Reads an edge list from a file and creates a graph.">igraph_read_graph_edgelist</a></strong></span>(&g, f, 0, IGRAPH_DIRECTED);
|
||
<span class="strong"><strong>fclose</strong></span>(f);
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_matrix_init" title="3.2.1. igraph_matrix_init — Initializes a matrix.">igraph_matrix_init</a></strong></span>(&coords, 0, 0);
|
||
<span class="strong"><strong><a class="link" href="igraph-Layout.html#igraph_layout_reingold_tilford" title="2.1. igraph_layout_reingold_tilford — Reingold-Tilford layout for tree graphs.">igraph_layout_reingold_tilford</a></strong></span>(&g, &coords, IGRAPH_IN, 0, 0);
|
||
<span class="strong"><strong>igraph_matrix_print</strong></span>(&coords);
|
||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_matrix_destroy" title="3.2.4. igraph_matrix_destroy — Destroys a matrix object.">igraph_matrix_destroy</a></strong></span>(&coords);
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||
|
||
<span class="strong"><strong>return</strong></span> 0;
|
||
}
|
||
</pre>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
<br class="example-break">
|
||
</div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_reingold_tilford_circular"></a>2.2. <code class="function">igraph_layout_reingold_tilford_circular</code> — Circular Reingold-Tilford layout for trees.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.3.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_reingold_tilford_circular(const igraph_t *graph,
|
||
igraph_matrix_t *res,
|
||
igraph_neimode_t mode,
|
||
const igraph_vector_int_t *roots,
|
||
const igraph_vector_int_t *rootlevel);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This layout is almost the same as <a class="link" href="igraph-Layout.html#igraph_layout_reingold_tilford" title="2.1. igraph_layout_reingold_tilford — Reingold-Tilford layout for tree graphs."><code class="function">igraph_layout_reingold_tilford()</code></a>, but
|
||
the tree is drawn in a circular way, with the root vertex in the center.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
The result, the coordinates in a matrix. The parameter
|
||
should point to an initialized matrix object and will be resized.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies which edges to consider when building the tree.
|
||
If it is <code class="constant">IGRAPH_OUT</code> then only the outgoing, if it is <code class="constant">IGRAPH_IN</code>
|
||
then only the incoming edges of a parent are considered. If it is
|
||
<code class="constant">IGRAPH_ALL</code> then all edges are used (this was the behavior in
|
||
igraph 0.5 and before). This parameter also influences how the root
|
||
vertices are calculated, if they are not given. See the <em class="parameter"><code>roots</code></em> parameter.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>roots</code></em>:</span></p></td>
|
||
<td><p>
|
||
The index of the root vertex or root vertices. The set of roots
|
||
should be specified so that all vertices of the graph are reachable from them.
|
||
Simply put, in the undirected case, one root should be given from each
|
||
connected component. If <em class="parameter"><code>roots</code></em> is <code class="constant">NULL</code> or a pointer to an empty vector,
|
||
then the roots will be selected automatically. Currently, automatic root
|
||
selection prefers low eccentricity vertices in graphs with fewer than
|
||
500 vertices, and high degree vertices (according to <em class="parameter"><code>mode</code></em>) in larger graphs.
|
||
The root selection heuristic may change without notice. To ensure a consistent
|
||
output, please specify the roots manually.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>rootlevel</code></em>:</span></p></td>
|
||
<td><p>
|
||
This argument can be useful when drawing forests which are
|
||
not trees (i.e. they are unconnected and have tree components). It specifies
|
||
the level of the root vertices for every tree in the forest. It is only
|
||
considered if not a null pointer and the <em class="parameter"><code>roots</code></em> argument is also given
|
||
(and it is not a null pointer or an empty vector).
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_reingold_tilford" title="2.1. igraph_layout_reingold_tilford — Reingold-Tilford layout for tree graphs."><code class="function">igraph_layout_reingold_tilford()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_roots_for_tree_layout"></a>2.3. <code class="function">igraph_roots_for_tree_layout</code> — Roots suitable for a nice tree layout.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.3.4.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_roots_for_tree_layout(
|
||
const igraph_t *graph,
|
||
igraph_neimode_t mode,
|
||
igraph_vector_int_t *roots,
|
||
igraph_root_choice_t heuristic);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function chooses a root, or a set of roots suitable for visualizing a tree,
|
||
or a tree-like graph. It is typically used with <a class="link" href="igraph-Layout.html#igraph_layout_reingold_tilford" title="2.1. igraph_layout_reingold_tilford — Reingold-Tilford layout for tree graphs."><code class="function">igraph_layout_reingold_tilford()</code></a>.
|
||
The principle is to select a minimal set of roots so that all other vertices
|
||
will be reachable from them.
|
||
|
||
</p>
|
||
<p>
|
||
In the undirected case, one root is chosen from each connected component.
|
||
In the directed case, one root is chosen from each strongly connected component
|
||
that has no incoming (or outgoing) edges (depending on 'mode'). When more than
|
||
one root choice is possible, vertices are prioritized based on the given <em class="parameter"><code>heuristic</code></em>.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The graph, typically a tree, but any graph is accepted.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to interpret the input as undirected, a directed out-tree or in-tree.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>roots</code></em>:</span></p></td>
|
||
<td><p>
|
||
An initialized integer vector, the roots will be returned here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>heuristic</code></em>:</span></p></td>
|
||
<td>
|
||
<p>
|
||
The heuristic to use for breaking ties when multiple root
|
||
choices are possible.
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_ROOT_CHOICE_DEGREE</code></span></p></td>
|
||
<td><p>
|
||
|
||
Choose the vertices with the highest degree (out- or in-degree
|
||
in directed mode). This simple heuristic is fast even in large graphs.
|
||
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_ROOT_CHOICE_ECCENTRICITY</code></span></p></td>
|
||
<td><p>
|
||
|
||
Choose the vertices with the lowest eccentricity. This usually results
|
||
in a "wide and shallow" tree layout. While this heuristic produces
|
||
high-quality results, it is slow for large graphs: computing the
|
||
eccentricities has quadratic complexity in the number of vertices.
|
||
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: depends on the heuristic.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_sugiyama"></a>2.4. <code class="function">igraph_layout_sugiyama</code> — Sugiyama layout algorithm for layered directed acyclic graphs.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.3.5.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_sugiyama(
|
||
const igraph_t *graph, igraph_matrix_t *res, igraph_matrix_list_t *routing,
|
||
const igraph_vector_int_t* layers, igraph_real_t hgap, igraph_real_t vgap,
|
||
igraph_int_t maxiter, const igraph_vector_t *weights
|
||
);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
This layout algorithm is designed for directed acyclic graphs where each
|
||
vertex is assigned to a layer. Layers are indexed from zero, and vertices
|
||
of the same layer will be placed on the same horizontal line. The X coordinates
|
||
of vertices within each layer are decided by the heuristic proposed by
|
||
Sugiyama et al to minimize edge crossings.
|
||
|
||
</p>
|
||
<p>
|
||
You can also try to lay out undirected graphs, graphs containing cycles, or
|
||
graphs without an a priori layered assignment with this algorithm. igraph
|
||
will try to eliminate cycles and assign vertices to layers, but there is no
|
||
guarantee on the quality of the layout in such cases.
|
||
|
||
</p>
|
||
<p>
|
||
The Sugiyama layout may introduce "bends" on the edges in order to obtain a
|
||
visually more pleasing layout. The additional control points of the edges are
|
||
returned in a separate list of matrices, one matrix per edge in the original
|
||
graph. If an edge requires no additional control points, the corresponding
|
||
matrix will be empty, otherwise the matrix will contain the coordinates of
|
||
the control points, one point per row. When drawing the graph, edges should
|
||
be drawn in a way that the curve representing the edge passes through the
|
||
control points.
|
||
|
||
</p>
|
||
<p>
|
||
For more details, see K. Sugiyama, S. Tagawa and M. Toda, "Methods for Visual
|
||
Understanding of Hierarchical Systems". IEEE Transactions on Systems, Man and
|
||
Cybernetics 11(2):109-125, 1981.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will contain
|
||
the result and will be resized as needed. The coordinates of the
|
||
vertices in the layout will be stored in the rows of the matrix,
|
||
one row per vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>routing</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an uninitialized list of matrices or <code class="constant">NULL</code>.
|
||
When not <code class="constant">NULL</code>, the list will be resized as needed such
|
||
that there will be one matrix for each edge of the graph,
|
||
and the matrix will hold the additional control points that
|
||
the edge must pass through, starting from the source vertex
|
||
of the edge and ending at the target vertex. The matrix will
|
||
have zero rows if an edge does not require control points.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>layers</code></em>:</span></p></td>
|
||
<td><p>
|
||
The layer index for each vertex or <code class="constant">NULL</code> if the layers should
|
||
be determined automatically by igraph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hgap</code></em>:</span></p></td>
|
||
<td><p>
|
||
The preferred minimum horizontal gap between vertices in the same
|
||
layer.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>vgap</code></em>:</span></p></td>
|
||
<td><p>
|
||
The distance between layers.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxiter</code></em>:</span></p></td>
|
||
<td><p>
|
||
Maximum number of iterations in the crossing minimization stage.
|
||
100 is a reasonable default; if you feel that you have too
|
||
many edge crossings, increase this.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Weights of the edges. These are used only if the graph contains
|
||
cycles; igraph will tend to reverse edges with smaller
|
||
weights when breaking the cycles.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_umap"></a>2.5. <code class="function">igraph_layout_umap</code> — Layout using Uniform Manifold Approximation and Projection (UMAP).</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.3.6.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_umap(const igraph_t *graph,
|
||
igraph_matrix_t *res,
|
||
igraph_bool_t use_seed,
|
||
const igraph_vector_t *distances,
|
||
igraph_real_t min_dist,
|
||
igraph_int_t epochs,
|
||
igraph_bool_t distances_are_weights);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<div class="warning" style="margin-left: 0.5in; margin-right: 0.5in;">
|
||
<h3 class="title">Warning</h3>
|
||
<p>This function is experimental and its signature is not considered final yet.
|
||
We reserve the right to change the function signature without changing the
|
||
major version of igraph. Use it at your own risk.</p>
|
||
</div>
|
||
<p>UMAP is mostly used to embed high-dimensional vectors in a low-dimensional space
|
||
(most commonly 2D). The algorithm is probabilistic and introduces nonlinearities,
|
||
unlike e.g. PCA and similar to T-distributed Stochastic Neighbor Embedding (t-SNE).
|
||
Nonlinearity helps "cluster" very similar vectors together without imposing a
|
||
global geometry on the embedded space (e.g. a rigid rotation + compression in PCA).
|
||
UMAP uses graphs as intermediate data structures, hence it can be used as a
|
||
graph layout algorithm as well.
|
||
|
||
</p>
|
||
<p>
|
||
The general UMAP workflow is to start from vectors, compute a sparse distance
|
||
graph that only contains edges between simiar points (e.g. a k-nearest neighbors
|
||
graph), and then convert these distances into exponentially decaying weights
|
||
between 0 and 1 that are larger for points that are closest neighbors in the
|
||
distance graph. If a graph without any distances associated to the edges is used,
|
||
all weights will be set to 1.
|
||
|
||
</p>
|
||
<p>
|
||
If you are trying to use this function to embed high-dimensional vectors, you should
|
||
first compute a k-nearest neighbors graph between your vectors and compute the
|
||
associated distances, and then call this function on that graph. If you already
|
||
have a distance graph, or you have a graph with no distances, you can call this
|
||
function directly. If you already have a graph with meaningful weights
|
||
associated to each edge, you can also call this function, but set the argument
|
||
<em class="parameter"><code>distances_are_weights</code></em> to true. To compute weights from distances
|
||
without computing the layout, see <a class="link" href="igraph-Layout.html#igraph_layout_umap_compute_weights" title="2.6. igraph_layout_umap_compute_weights — Compute weights for a UMAP layout starting from distances."><code class="function">igraph_layout_umap_compute_weights()</code></a>.
|
||
|
||
</p>
|
||
<p>
|
||
References:
|
||
|
||
</p>
|
||
<p>
|
||
Leland McInnes, John Healy, and James Melville:
|
||
UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2020)
|
||
<a class="ulink" href="https://arxiv.org/abs/1802.03426" target="_top">https://arxiv.org/abs/1802.03426</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the graph to find a layout for (i.e. to embed). This is
|
||
typically a sparse graph with only edges for the shortest distances stored, e.g.
|
||
a k-nearest neighbors graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the n by 2 matrix where the layout coordinates will be stored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
If <code class="constant">true</code> the supplied values in the <em class="parameter"><code>res</code></em> argument are
|
||
used as an initial layout, if <code class="constant">false</code> a random initial layout is used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>distances</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector of distances associated with the graph edges.
|
||
If this argument is <code class="constant">NULL</code>, all weights will be set to 1.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_dist</code></em>:</span></p></td>
|
||
<td><p>
|
||
A fudge parameter that decides how close two unconnected vertices
|
||
can be in the embedding before feeling a repulsive force. It must not be
|
||
negative. Typical values are between 0 and 1.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>epochs</code></em>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations of the main stochastic gradient descent loop on
|
||
the cross-entropy. Typical values are between 30 and 500.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>distances_are_weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to use precomputed weights. If
|
||
true, the <em class="parameter"><code>distances</code></em> vector contains precomputed weights. If <code class="constant">false</code> (the
|
||
typical use case), this function will compute weights from distances and
|
||
then use them to compute the layout.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_umap_3d" title="3.6. igraph_layout_umap_3d — 3D layout using UMAP."><code class="function">igraph_layout_umap_3d()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_umap_compute_weights"></a>2.6. <code class="function">igraph_layout_umap_compute_weights</code> — Compute weights for a UMAP layout starting from distances.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.3.7.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_umap_compute_weights(
|
||
const igraph_t *graph,
|
||
const igraph_vector_t *distances,
|
||
igraph_vector_t *weights);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<div class="warning" style="margin-left: 0.5in; margin-right: 0.5in;">
|
||
<h3 class="title">Warning</h3>
|
||
<p>This function is experimental and its signature is not considered final yet.
|
||
We reserve the right to change the function signature without changing the
|
||
major version of igraph. Use it at your own risk.</p>
|
||
</div>
|
||
<p>UMAP is used to embed high-dimensional vectors in a low-dimensional space
|
||
(most commonly 2D). It uses a distance graph as an intermediate data structure,
|
||
making it also a useful graph layout algorithm. See <a class="link" href="igraph-Layout.html#igraph_layout_umap" title="2.5. igraph_layout_umap — Layout using Uniform Manifold Approximation and Projection (UMAP)."><code class="function">igraph_layout_umap()</code></a>
|
||
for more information.
|
||
|
||
</p>
|
||
<p>
|
||
An early step in UMAP is to compute exponentially decaying "weights" from the
|
||
distance graph. Connectivities can also be viewed as edge weights that quantify
|
||
similarity between two vertices. This function computes weights from the
|
||
distance graph. To compute the layout from precomputed weights, call
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_umap" title="2.5. igraph_layout_umap — Layout using Uniform Manifold Approximation and Projection (UMAP)."><code class="function">igraph_layout_umap()</code></a> with the <em class="parameter"><code>distances_are_weights</code></em> argument set to <code class="constant">true</code>.
|
||
|
||
</p>
|
||
<p>
|
||
While the distance graph can be directed (e.g. in a k-nearest neighbors, it is
|
||
clear <span class="emphasis"><em>whom</em></span> you are a neighbor of), the weights are usually undirected. Whenever two
|
||
vertices are doubly connected in the distance graph, the resulting weight <code class="constant">W</code> is set as:
|
||
|
||
</p>
|
||
<p>
|
||
<code class="literal">W = W1 + W2 - W1 * W2</code>
|
||
|
||
Because UMAP weights are interpreted as probabilities, this is just the probability
|
||
that either edge is present, without double counting. It is called "fuzzy union" in
|
||
the original UMAP implementation and is the default. One could also require that both
|
||
edges are there, i.e. W = W1 * W2: this would represent the fuzzy intersection and is
|
||
not implemented in igraph. As a consequence of this symmetrization, information is lost,
|
||
i.e. one needs fewer weights than one had distances. To keep things efficient, here
|
||
we set the weight for one of the two edges as above and the weight for its opposite edge
|
||
as 0, so that it will be skipped in the UMAP gradient descent later on.
|
||
|
||
</p>
|
||
<p>
|
||
Technical note: For each vertex, this function computes its scale factor (sigma),
|
||
its connectivity correction (rho), and finally the weights themselves.
|
||
|
||
</p>
|
||
<p>
|
||
References:
|
||
|
||
</p>
|
||
<p>
|
||
Leland McInnes, John Healy, and James Melville:
|
||
UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2020)
|
||
<a class="ulink" href="https://arxiv.org/abs/1802.03426" target="_top">https://arxiv.org/abs/1802.03426</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the distance graph. This can be directed (e.g. connecting
|
||
each vertex to its neighbors in a k-nearest neighbor) or undirected, but must
|
||
have no loops nor parallel edges. The only exception is: if the graph is directed,
|
||
having pairs of edges with opposite direction is accepted.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>distances</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the vector with the vertex-to-vertex distance associated with
|
||
each edge. This argument can be NULL, in which case all edges are assumed to have the
|
||
same distance.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized vector where the result will be stored. If the
|
||
input graph is directed, the weights represent a symmetrized version which contains
|
||
less information. Therefore, whenever two edges between the same vertices and opposite
|
||
direction are present in the input graph, only one of the weights is set and the other
|
||
is fixed to zero. That format is accepted by <a class="link" href="igraph-Layout.html#igraph_layout_umap" title="2.5. igraph_layout_umap — Layout using Uniform Manifold Approximation and Projection (UMAP)."><code class="function">igraph_layout_umap()</code></a>, which skips
|
||
all zero-weight edges from the layout optimization.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_umap" title="2.5. igraph_layout_umap — Layout using Uniform Manifold Approximation and Projection (UMAP)."><code class="function">igraph_layout_umap()</code></a>, <a class="link" href="igraph-Layout.html#igraph_layout_umap_3d" title="3.6. igraph_layout_umap_3d — 3D layout using UMAP."><code class="function">igraph_layout_umap_3d()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="three-d-layout-generators"></a>3. 3D layout generators</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_random_3d">3.1. <code class="function">igraph_layout_random_3d</code> — Places the vertices uniformly randomly in a cube.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_sphere">3.2. <code class="function">igraph_layout_sphere</code> — Places vertices (more or less) uniformly on a sphere.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_grid_3d">3.3. <code class="function">igraph_layout_grid_3d</code> — Places the vertices on a regular grid in the 3D space.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_fruchterman_reingold_3d">3.4. <code class="function">igraph_layout_fruchterman_reingold_3d</code> — 3D Fruchterman-Reingold algorithm.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_kamada_kawai_3d">3.5. <code class="function">igraph_layout_kamada_kawai_3d</code> — 3D version of the Kamada-Kawai layout generator.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_umap_3d">3.6. <code class="function">igraph_layout_umap_3d</code> — 3D layout using UMAP.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_random_3d"></a>3.1. <code class="function">igraph_layout_random_3d</code> — Places the vertices uniformly randomly in a cube.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.4.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_random_3d(const igraph_t *graph, igraph_matrix_t *res);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
Vertex coordinates range from -1 to 1, and are placed in three columns
|
||
of a matrix, with a row for each vertex.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The graph to place.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. It will be
|
||
resized to hold the result.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Added in version 0.2.</p>
|
||
<p>
|
||
|
||
Time complexity: O(|V|), the number of vertices.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_sphere"></a>3.2. <code class="function">igraph_layout_sphere</code> — Places vertices (more or less) uniformly on a sphere.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.4.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_sphere(const igraph_t *graph, igraph_matrix_t *res);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
The vertices are placed with approximately equal spacing on a spiral
|
||
wrapped around a sphere, in the order of their vertex IDs. Vertices
|
||
with consecutive vertex IDs are placed near each other.
|
||
|
||
</p>
|
||
<p>
|
||
The algorithm was described in the following paper:
|
||
|
||
</p>
|
||
<p>
|
||
Distributing many points on a sphere by E.B. Saff and
|
||
A.B.J. Kuijlaars, <span class="emphasis"><em> Mathematical Intelligencer </em></span> 19.1 (1997)
|
||
5--11. <a class="ulink" href="https://doi.org/10.1007/BF03024331" target="_top">https://doi.org/10.1007/BF03024331</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will
|
||
contain the result and will be resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code. The current implementation always returns with
|
||
success.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Added in version 0.2.</p>
|
||
<p>
|
||
|
||
Time complexity: O(|V|), the number of vertices in the graph.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_grid_3d"></a>3.3. <code class="function">igraph_layout_grid_3d</code> — Places the vertices on a regular grid in the 3D space.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.4.4.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_grid_3d(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_int_t width, igraph_int_t height);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will
|
||
contain the result and will be resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>width</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of vertices in a single row of the grid. When
|
||
zero or negative, the width is determined automatically.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>height</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of vertices in a single column of the grid. When
|
||
zero or negative, the height is determined automatically.</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code. The current implementation always returns with
|
||
success.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|), the number of vertices.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_fruchterman_reingold_3d"></a>3.4. <code class="function">igraph_layout_fruchterman_reingold_3d</code> — 3D Fruchterman-Reingold algorithm.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.4.5.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_fruchterman_reingold_3d(const igraph_t *graph,
|
||
igraph_matrix_t *res,
|
||
igraph_bool_t use_seed,
|
||
igraph_int_t niter,
|
||
igraph_real_t start_temp,
|
||
const igraph_vector_t *weights,
|
||
const igraph_vector_t *minx,
|
||
const igraph_vector_t *maxx,
|
||
const igraph_vector_t *miny,
|
||
const igraph_vector_t *maxy,
|
||
const igraph_vector_t *minz,
|
||
const igraph_vector_t *maxz);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This is the 3D version of the force based Fruchterman-Reingold layout.
|
||
See <a class="link" href="igraph-Layout.html#igraph_layout_fruchterman_reingold" title="1.8. igraph_layout_fruchterman_reingold — Places the vertices on a plane according to the Fruchterman-Reingold algorithm."><code class="function">igraph_layout_fruchterman_reingold()</code></a> for the 2D version.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will
|
||
contain the result and will be resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
If true the supplied values in the
|
||
<em class="parameter"><code>res</code></em> argument are used as an initial layout, if
|
||
false a random initial layout is used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>niter</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of iterations to do. A reasonable
|
||
default value is 500.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>start_temp</code></em>:</span></p></td>
|
||
<td><p>
|
||
Start temperature. This is the maximum amount
|
||
of movement alloved along one axis, within one step, for a
|
||
vertex. Currently it is decreased linearly to zero during
|
||
the iteration.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector containing edge weights. Weights must
|
||
be positive. If <code class="constant">NULL</code>, all edges are assumed to have weight 1.
|
||
The attraction along the edges will be multiplied by the weights,
|
||
resulting in vertices connected by a high-weight edge being placed
|
||
closer together.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>minx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">x</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>minx</code></em>, but the maximum <span class="quote">“<span class="quote">x</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>miny</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">y</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxy</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>miny</code></em>, but the maximum <span class="quote">“<span class="quote">y</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>minz</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">z</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxz</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>minz</code></em>, but the maximum <span class="quote">“<span class="quote">z</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Added in version 0.2.</p>
|
||
<p>
|
||
|
||
Time complexity: O(|V|^2) in each
|
||
iteration, |V| is the number of
|
||
vertices in the graph.
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_kamada_kawai_3d"></a>3.5. <code class="function">igraph_layout_kamada_kawai_3d</code> — 3D version of the Kamada-Kawai layout generator.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.4.6.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_kamada_kawai_3d(const igraph_t *graph, igraph_matrix_t *res,
|
||
igraph_bool_t use_seed, igraph_int_t maxiter,
|
||
igraph_real_t epsilon, igraph_real_t kkconst,
|
||
const igraph_vector_t *weights,
|
||
const igraph_vector_t *minx, const igraph_vector_t *maxx,
|
||
const igraph_vector_t *miny, const igraph_vector_t *maxy,
|
||
const igraph_vector_t *minz, const igraph_vector_t *maxz);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
This is the 3D version of <a class="link" href="igraph-Layout.html#igraph_layout_kamada_kawai" title="1.9. igraph_layout_kamada_kawai — Places the vertices on a plane according to the Kamada-Kawai algorithm."><code class="function">igraph_layout_kamada_kawai()</code></a>.
|
||
See the documentation of that function for more information.
|
||
|
||
</p>
|
||
<p>
|
||
This layout algorithm is not suitable for large graphs. The memory
|
||
requirements are of the order O(|V|^2).
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
A graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object. This will
|
||
contain the result (x-, y- and z-positions in columns one
|
||
through three) and will be resized if needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, whether to use the values supplied in the
|
||
<em class="parameter"><code>res</code></em> argument as the initial configuration. If zero and there
|
||
are any limits on the z, y or z coordinates, then a random initial
|
||
configuration is used. Otherwise the vertices are placed uniformly
|
||
on a sphere of radius 1 as the initial configuration.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxiter</code></em>:</span></p></td>
|
||
<td><p>
|
||
The maximum number of iterations to perform. A reasonable
|
||
default value is at least ten (or more) times the number of
|
||
vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>epsilon</code></em>:</span></p></td>
|
||
<td><p>
|
||
Stop the iteration, if the maximum delta value of the
|
||
algorithm is smaller than this. It is safe to leave it at zero,
|
||
and then <em class="parameter"><code>maxiter</code></em> iterations are performed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>kkconst</code></em>:</span></p></td>
|
||
<td><p>
|
||
The Kamada-Kawai vertex attraction constant.
|
||
Typical value: number of vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
A vector of edge weights. Weights are interpreted as edge
|
||
<span class="emphasis"><em>lengths</em></span> in the shortest path calculation used by the
|
||
Kamada-Kawai algorithm. Therefore, vertices connected by high-weight
|
||
edges will be placed further apart. Pass <code class="constant">NULL</code> to assume unit weights
|
||
for all edges.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>minx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">x</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxx</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>minx</code></em>, but the maximum <span class="quote">“<span class="quote">x</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>miny</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">y</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxy</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>miny</code></em>, but the maximum <span class="quote">“<span class="quote">y</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>minz</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a <code class="constant">NULL</code> pointer. If not a
|
||
<code class="constant">NULL</code> pointer then the vector gives the minimum
|
||
<span class="quote">“<span class="quote">z</span>”</span> coordinate for every vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maxz</code></em>:</span></p></td>
|
||
<td><p>
|
||
Same as <em class="parameter"><code>minz</code></em>, but the maximum <span class="quote">“<span class="quote">z</span>”</span>
|
||
coordinates.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|) for each iteration, after an O(|V|^2
|
||
log|V|) initialization step. |V| is the number of vertices in the
|
||
graph.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_umap_3d"></a>3.6. <code class="function">igraph_layout_umap_3d</code> — 3D layout using UMAP.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.4.7.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_umap_3d(const igraph_t *graph,
|
||
igraph_matrix_t *res,
|
||
igraph_bool_t use_seed,
|
||
const igraph_vector_t *distances,
|
||
igraph_real_t min_dist,
|
||
igraph_int_t epochs,
|
||
igraph_bool_t distances_are_weights);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<div class="warning" style="margin-left: 0.5in; margin-right: 0.5in;">
|
||
<h3 class="title">Warning</h3>
|
||
<p>This function is experimental and its signature is not considered final yet.
|
||
We reserve the right to change the function signature without changing the
|
||
major version of igraph. Use it at your own risk.</p>
|
||
</div>
|
||
<p>This is the 3D version of the UMAP algorithm
|
||
(see <a class="link" href="igraph-Layout.html#igraph_layout_umap" title="2.5. igraph_layout_umap — Layout using Uniform Manifold Approximation and Projection (UMAP)."><code class="function">igraph_layout_umap()</code></a> for the 2D version).
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the graph to find a layout for (i.e. to embed). This is
|
||
typically a directed, sparse graph with only edges for the shortest distances
|
||
stored, e.g. a k-nearest neighbors graph with the edges going from each focal
|
||
vertex to its neighbors. However, it can also be an undirected graph. If the
|
||
<em class="parameter"><code>distances_are_weights</code></em> is <code class="constant">true</code>, this is treated as an undirected graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the n by 3 matrix where the layout coordinates will be stored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>use_seed</code></em>:</span></p></td>
|
||
<td><p>
|
||
If true the supplied values in the <em class="parameter"><code>res</code></em> argument are used
|
||
as an initial layout, if false a random initial layout is used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>distances</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector of distances associated with the graph edges.
|
||
If this argument is <code class="constant">NULL</code>, all edges are assumed to have the same distance.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_dist</code></em>:</span></p></td>
|
||
<td><p>
|
||
A fudge parameter that decides how close two unconnected vertices
|
||
can be in the embedding before feeling a repulsive force. It must not be
|
||
negative. Typical values are between 0 and 1.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>epochs</code></em>:</span></p></td>
|
||
<td><p>
|
||
Number of iterations of the main stochastic gradient descent loop on
|
||
the cross-entropy. Typical values are between 30 and 500.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>distances_are_weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to use precomputed weights. If <code class="constant">false</code> (the
|
||
typical use case), this function will compute weights from distances and
|
||
then use them to compute the layout. If <code class="constant">true</code>, the <em class="parameter"><code>distances</code></em> vector contains
|
||
precomputed weights, including possibly some weights equal to zero that are
|
||
inconsequential for the layout optimization.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_umap" title="2.5. igraph_layout_umap — Layout using Uniform Manifold Approximation and Projection (UMAP)."><code class="function">igraph_layout_umap()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="pp-layouts"></a>4. Post-processing layouts</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_merge_dla">4.1. <code class="function">igraph_layout_merge_dla</code> — Merges multiple layouts by using a DLA algorithm.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Layout.html#igraph_layout_align">4.2. <code class="function">igraph_layout_align</code> — Aligns a graph layout with the coordinate axes.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_merge_dla"></a>4.1. <code class="function">igraph_layout_merge_dla</code> — Merges multiple layouts by using a DLA algorithm.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.5.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_merge_dla(
|
||
const igraph_vector_ptr_t *thegraphs, const igraph_matrix_list_t *coords,
|
||
igraph_matrix_t *res
|
||
);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
First each layout is covered by a circle. Then the layout of the
|
||
largest graph is placed at the origin. Then the other layouts are
|
||
placed by the DLA algorithm, larger ones first and smaller ones
|
||
last.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>thegraphs</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer vector containing the graph objects of
|
||
which the layouts will be merged.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>coords</code></em>:</span></p></td>
|
||
<td><p>
|
||
List of matrices with the 2D layouts of the graphs in <em class="parameter"><code>thegraphs</code></em>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix object, the result will
|
||
be stored here. It will be resized if needed.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Added in version 0.2.
|
||
|
||
</p>
|
||
<p>
|
||
Time complexity: TODO.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_layout_align"></a>4.2. <code class="function">igraph_layout_align</code> — Aligns a graph layout with the coordinate axes.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.30.5.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_layout_align(const igraph_t *graph, igraph_matrix_t *layout);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
This function centers a vertex layout on the coordinate system origin and
|
||
rotates the layout to achieve a visually pleasing alignment with the coordinate
|
||
axes. Doing this is particularly useful with force-directed layouts such as
|
||
<a class="link" href="igraph-Layout.html#igraph_layout_fruchterman_reingold" title="1.8. igraph_layout_fruchterman_reingold — Places the vertices on a plane according to the Fruchterman-Reingold algorithm."><code class="function">igraph_layout_fruchterman_reingold()</code></a>. Layouts in arbitrary dimensional
|
||
spaces are supported.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The graph whose layout is to be aligned.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>layout</code></em>:</span></p></td>
|
||
<td><p>
|
||
A matrix whose rows are the coordinates of vertices. It will
|
||
be modified in-place.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|E| + |V|), linear in the number of edges and vertices.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||
<td align="left"><a accesskey="p" href="igraph-Embedding.html"><b>← Chapter 28. Embedding of graphs</b></a></td>
|
||
<td align="right"><a accesskey="n" href="igraph-Processes.html"><b>Chapter 30. Processes on graphs →</b></a></td>
|
||
</tr></table>
|
||
</body>
|
||
</html>
|