Abdelrahman Said
1068 lines
38 KiB
HTML
1068 lines
38 KiB
HTML
<html>
|
||
<head>
|
||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||
<title>Chapter 27. Hierarchical random graphs</title>
|
||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
|
||
<link rel="home" href="index.html" title="igraph Reference Manual">
|
||
<link rel="up" href="index.html" title="igraph Reference Manual">
|
||
<link rel="prev" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||
<link rel="next" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||
<script type="text/javascript" src="toggle.js"></script><link rel="stylesheet" href="style.css" type="text/css">
|
||
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" type="text/css">
|
||
<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||
<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||
<link rel="index" href="ix01.html" title="Index">
|
||
</head>
|
||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||
<div class="navigation-header mb-4" width="100%" summary="Navigation header"><div class="btn-group">
|
||
<a accesskey="p" class="btn btn-light" href="igraph-Graphlets.html"><i class="fa fa-chevron-left"></i>
|
||
Previous
|
||
</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
|
||
Home
|
||
</a><a accesskey="n" class="btn btn-light" href="igraph-Embedding.html"><i class="fa fa-chevron-right"></i>
|
||
Next
|
||
</a>
|
||
</div></div>
|
||
<div class="chapter">
|
||
<div class="titlepage"><div><div><h1 class="title">
|
||
<a name="igraph-HRG"></a>Chapter 27. Hierarchical random graphs</h1></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-HRG.html#hrg-intro">1. Introduction</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#representing-hrgs">2. Representing HRGs</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#fitting-hrgs">3. Fitting HRGs</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#hrg-sampling">4. HRG sampling</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#conversion-to-and-from-igraph-graphs">5. Conversion to and from igraph graphs</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#predicting-missing-edges">6. Predicting missing edges</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#hrg-deprecated">7. Deprecated functions</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="hrg-intro"></a>1. Introduction</h2></div></div></div>
|
||
<p>A hierarchical random graph is an ensemble of undirected
|
||
graphs with <code class="constant">n</code> vertices. It is defined via a binary tree with <code class="constant">n</code> leaf and <code class="constant">n-1</code> internal vertices, where the
|
||
internal vertices are labeled with probabilities.
|
||
The probability that two vertices are connected in the random graph
|
||
is given by the probability label at their closest common
|
||
ancestor.
|
||
</p>
|
||
<p>Please read the following two articles for more about
|
||
hierarchical random graphs: A. Clauset, C. Moore, and M.E.J. Newman.
|
||
Hierarchical structure and the prediction of missing links in networks.
|
||
Nature 453, 98 - 101 (2008); and A. Clauset, C. Moore, and M.E.J. Newman.
|
||
Structural Inference of Hierarchies in Networks. In E. M. Airoldi
|
||
et al. (Eds.): ICML 2006 Ws, Lecture Notes in Computer Science
|
||
4503, 1-13. Springer-Verlag, Berlin Heidelberg (2007).
|
||
</p>
|
||
<p>
|
||
igraph contains functions for fitting HRG models to a given network
|
||
(<a class="link" href="igraph-HRG.html#igraph_hrg_fit" title="3.1. igraph_hrg_fit — Fit a hierarchical random graph model to a network."><code class="function">igraph_hrg_fit</code></a>), for generating networks from a given HRG
|
||
ensemble (<a class="link" href="igraph-HRG.html#igraph_hrg_game" title="4.2. igraph_hrg_game — Generate a hierarchical random graph."><code class="function">igraph_hrg_game</code></a>, <a class="link" href="igraph-HRG.html#igraph_hrg_sample" title="4.1. igraph_hrg_sample — Sample from a hierarchical random graph model."><code class="function">igraph_hrg_sample</code></a>), converting
|
||
an igraph graph to a HRG and back (<a class="link" href="igraph-HRG.html#igraph_hrg_create" title="5.2. igraph_hrg_create — Create a HRG from an igraph graph."><code class="function">igraph_hrg_create</code></a>, <a class="link" href="igraph-HRG.html#igraph_hrg_dendrogram" title="7.1. igraph_hrg_dendrogram — Create a dendrogram from a hierarchical random graph."><code class="function">igraph_hrg_dendrogram</code></a>), for calculating a consensus tree from a
|
||
set of sampled HRGs (<a class="link" href="igraph-HRG.html#igraph_hrg_consensus" title="3.2. igraph_hrg_consensus — Calculate a consensus tree for a HRG."><code class="function">igraph_hrg_consensus</code></a>) and for predicting
|
||
missing edges in a network based on its HRG models (<a class="link" href="igraph-HRG.html#igraph_hrg_predict" title="6.1. igraph_hrg_predict — Predict missing edges in a graph, based on HRG models."><code class="function">igraph_hrg_predict</code></a>).
|
||
</p>
|
||
<p>The igraph HRG implementation is heavily based on the code
|
||
published by Aaron Clauset, at his website,
|
||
<a class="ulink" href="https://aaronclauset.github.io/hierarchy/" target="_top">https://aaronclauset.github.io/hierarchy/</a>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="representing-hrgs"></a>2. Representing HRGs</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_t">2.1. <code class="function">igraph_hrg_t</code> — Data structure to store a hierarchical random graph.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_init">2.2. <code class="function">igraph_hrg_init</code> — Allocate memory for a HRG.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_destroy">2.3. <code class="function">igraph_hrg_destroy</code> — Deallocate memory for an HRG.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_size">2.4. <code class="function">igraph_hrg_size</code> — Returns the size of the HRG, the number of leaf nodes.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_resize">2.5. <code class="function">igraph_hrg_resize</code> — Resize a HRG.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_t"></a>2.1. <code class="function">igraph_hrg_t</code> — Data structure to store a hierarchical random graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.3.2.2"></a><p>
|
||
</p>
|
||
<pre class="programlisting">
|
||
typedef struct igraph_hrg_t {
|
||
igraph_vector_int_t left;
|
||
igraph_vector_int_t right;
|
||
igraph_vector_t prob;
|
||
igraph_vector_int_t vertices;
|
||
igraph_vector_int_t edges;
|
||
} igraph_hrg_t;
|
||
</pre>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
</p>
|
||
<p>A hierarchical random graph (HRG) can be given as a binary tree,
|
||
where the internal vertices are labeled with real numbers.
|
||
|
||
</p>
|
||
<p>Note that you don't necessarily have to know this
|
||
internal representation for using the HRG functions, just pass the
|
||
HRG objects created by one igraph function, to another igraph
|
||
function.
|
||
|
||
</p>
|
||
<p>
|
||
It has the following members:
|
||
|
||
</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">left</code>:</span></p></td>
|
||
<td><p>
|
||
Vector that contains the left children of the internal
|
||
tree vertices. The first vertex is always the root vertex, so
|
||
the first element of the vector is the left child of the root
|
||
vertex. Internal vertices are denoted with negative numbers,
|
||
starting from -1 and going down, i.e. the root vertex is
|
||
-1. Leaf vertices are denoted by non-negative number, starting
|
||
from zero and up.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">right</code>:</span></p></td>
|
||
<td><p>
|
||
Vector that contains the right children of the
|
||
vertices, with the same encoding as the <code class="constant">left</code> vector.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">prob</code>:</span></p></td>
|
||
<td><p>
|
||
The connection probabilities attached to the internal
|
||
vertices, the first number belongs to the root vertex
|
||
(i.e. internal vertex -1), the second to internal vertex -2,
|
||
etc.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">edges</code>:</span></p></td>
|
||
<td><p>
|
||
The number of edges in the subtree below the given
|
||
internal vertex.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">vertices</code>:</span></p></td>
|
||
<td><p>
|
||
The number of vertices in the subtree below the
|
||
given internal vertex, including itself.</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_init"></a>2.2. <code class="function">igraph_hrg_init</code> — Allocate memory for a HRG.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.3.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_init(igraph_hrg_t *hrg, igraph_int_t n);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function must be called before passing an <a class="link" href="igraph-HRG.html#igraph_hrg_t" title="2.1. igraph_hrg_t — Data structure to store a hierarchical random graph."><code class="function">igraph_hrg_t</code></a> to
|
||
an igraph function.
|
||
|
||
</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>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the HRG data structure to initialize.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of vertices in the graph that is modeled by
|
||
this HRG. It can be zero, if this is not yet known.
|
||
</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), the number of vertices in the graph.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_destroy"></a>2.3. <code class="function">igraph_hrg_destroy</code> — Deallocate memory for an HRG.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.3.4.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
void igraph_hrg_destroy(igraph_hrg_t *hrg);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
The HRG data structure can be reinitialized again with an <a class="link" href="igraph-HRG.html#igraph_hrg_destroy" title="2.3. igraph_hrg_destroy — Deallocate memory for an HRG."><code class="function">igraph_hrg_destroy</code></a> call.
|
||
|
||
</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>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the HRG data structure to deallocate.</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
|
||
Time complexity: operating system dependent.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_size"></a>2.4. <code class="function">igraph_hrg_size</code> — Returns the size of the HRG, the number of leaf nodes.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.3.5.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_int_t igraph_hrg_size(const igraph_hrg_t *hrg);
|
||
</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>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the HRG.
|
||
</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>
|
||
The number of leaf nodes in the HRG.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(1).
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_resize"></a>2.5. <code class="function">igraph_hrg_resize</code> — Resize a HRG.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.3.6.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_resize(igraph_hrg_t *hrg, igraph_int_t newsize);
|
||
</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>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized (see <a class="link" href="igraph-HRG.html#igraph_hrg_init" title="2.2. igraph_hrg_init — Allocate memory for a HRG."><code class="function">igraph_hrg_init</code></a>)
|
||
HRG.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>newsize</code></em>:</span></p></td>
|
||
<td><p>
|
||
The new size, i.e. the number of leaf nodes.
|
||
</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), n is the new size.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="fitting-hrgs"></a>3. Fitting HRGs</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_fit">3.1. <code class="function">igraph_hrg_fit</code> — Fit a hierarchical random graph model to a network.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_consensus">3.2. <code class="function">igraph_hrg_consensus</code> — Calculate a consensus tree for a HRG.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_fit"></a>3.1. <code class="function">igraph_hrg_fit</code> — Fit a hierarchical random graph model to a network.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.4.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_fit(const igraph_t *graph,
|
||
igraph_hrg_t *hrg,
|
||
igraph_bool_t start,
|
||
igraph_int_t steps);
|
||
</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>
|
||
The igraph graph to fit the model to. Edge directions
|
||
are ignored in directed graphs.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized HRG, the result of the fitting
|
||
is stored here. It can also be used to pass a HRG to the
|
||
function, that can be used as the starting point of the Markov
|
||
Chain Monte Carlo fitting, if the <em class="parameter"><code>start</code></em> argument is true.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>start</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to start the fitting from the given
|
||
HRG model.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>steps</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer, the number of MCMC steps to take in the
|
||
fitting procedure. If this is zero, then the fitting stops if a
|
||
convergence criteria is fulfilled.
|
||
</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: TODO.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_consensus"></a>3.2. <code class="function">igraph_hrg_consensus</code> — Calculate a consensus tree for a HRG.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.4.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_consensus(const igraph_t *graph,
|
||
igraph_vector_int_t *parents,
|
||
igraph_vector_t *weights,
|
||
igraph_hrg_t *hrg,
|
||
igraph_bool_t start,
|
||
igraph_int_t num_samples);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
The calculation can be started from the given HRG (<em class="parameter"><code>hrg</code></em>), or (if
|
||
<em class="parameter"><code>start</code></em> is false), a HRG is first fitted to the given graph.
|
||
|
||
</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>parents</code></em>:</span></p></td>
|
||
<td><p>
|
||
An initialized vector, the results are stored
|
||
here. For each vertex, the id of its parent vertex is stored, or
|
||
-1, if the vertex is the root vertex in the tree. The first n
|
||
vertex IDs (from 0) refer to the original vertices of the graph,
|
||
the other IDs refer to vertex groups.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Numeric vector, counts the number of times a given
|
||
tree split occured in the generated network samples, for each
|
||
internal vertices. The order is the same as in <em class="parameter"><code>parents</code></em>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
A hierarchical random graph. It is used as a starting
|
||
point for the sampling, if the <em class="parameter"><code>start</code></em> argument is true. It is
|
||
modified along the MCMC.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>start</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to use the supplied HRG (in <em class="parameter"><code>hrg</code></em>)
|
||
as a starting point for the MCMC.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>num_samples</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of samples to generate for creating
|
||
the consensus tree.
|
||
</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: TODO.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="hrg-sampling"></a>4. HRG sampling</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_sample">4.1. <code class="function">igraph_hrg_sample</code> — Sample from a hierarchical random graph model.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_game">4.2. <code class="function">igraph_hrg_game</code> — Generate a hierarchical random graph.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_sample"></a>4.1. <code class="function">igraph_hrg_sample</code> — Sample from a hierarchical random graph model.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.5.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_sample(const igraph_hrg_t *hrg, igraph_t *sample);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function draws a single sample from a hierarchical random graph model.
|
||
|
||
</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>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
A HRG model to sample from
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>sample</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an uninitialized graph; the sample is stored 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>
|
||
|
||
Time complexity: TODO.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_game"></a>4.2. <code class="function">igraph_hrg_game</code> — Generate a hierarchical random graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.5.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_game(igraph_t *graph,
|
||
const igraph_hrg_t *hrg);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function is a simple shortcut to <a class="link" href="igraph-HRG.html#igraph_hrg_sample" title="4.1. igraph_hrg_sample — Sample from a hierarchical random graph model."><code class="function">igraph_hrg_sample</code></a>.
|
||
It creates a single graph from the given HRG.
|
||
|
||
</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 uninitialized graph, the new graph is
|
||
created here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
The hierarchical random graph model to sample from.
|
||
</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: TODO.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="conversion-to-and-from-igraph-graphs"></a>5. Conversion to and from igraph graphs</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_from_hrg_dendrogram">5.1. <code class="function">igraph_from_hrg_dendrogram</code> — Create a graph representation of the dendrogram of a hierarchical random graph model.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_create">5.2. <code class="function">igraph_hrg_create</code> — Create a HRG from an igraph graph.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_from_hrg_dendrogram"></a>5.1. <code class="function">igraph_from_hrg_dendrogram</code> — Create a graph representation of the dendrogram of a hierarchical random graph model.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.6.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_from_hrg_dendrogram(
|
||
igraph_t *graph, const igraph_hrg_t *hrg, igraph_vector_t *prob
|
||
);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
Creates the igraph graph equivalent of the dendrogram encoded in an
|
||
<a class="link" href="igraph-HRG.html#igraph_hrg_t" title="2.1. igraph_hrg_t — Data structure to store a hierarchical random graph."><code class="function">igraph_hrg_t</code></a> data structure. The probabilities associated to the
|
||
nodes are returned in a vector so this function works without an
|
||
attribute handler.
|
||
|
||
</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 uninitialized graph, the result is
|
||
stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
The hierarchical random graph to convert.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>prob</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <span class="emphasis"><em>initialized</em></span> vector; the probabilities
|
||
associated to the nodes of the dendrogram will be stored here. Leaf nodes
|
||
will have an associated probability of <code class="constant">IGRAPH_NAN</code> .
|
||
You may set this to <code class="constant">NULL</code> if you do not need the probabilities.
|
||
</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), the number of vertices in the graph.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_create"></a>5.2. <code class="function">igraph_hrg_create</code> — Create a HRG from an igraph graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.6.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_create(igraph_hrg_t *hrg,
|
||
const igraph_t *graph,
|
||
const igraph_vector_t *prob);
|
||
</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>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized <a class="link" href="igraph-HRG.html#igraph_hrg_t" title="2.1. igraph_hrg_t — Data structure to store a hierarchical random graph."><code class="function">igraph_hrg_t</code></a>. The result
|
||
is stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The igraph graph to convert. It must be a directed
|
||
binary tree, with n-1 internal and n leaf vertices. The root
|
||
vertex must have in-degree zero.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>prob</code></em>:</span></p></td>
|
||
<td><p>
|
||
The vector of probabilities, this is used to label the
|
||
internal nodes of the hierarchical random graph.
|
||
</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), the number of vertices in the tree.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="predicting-missing-edges"></a>6. Predicting missing edges</h2></div></div></div>
|
||
<div class="toc"><dl class="toc"><dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_predict">6.1. <code class="function">igraph_hrg_predict</code> — Predict missing edges in a graph, based on HRG models.</a></span></dt></dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_predict"></a>6.1. <code class="function">igraph_hrg_predict</code> — Predict missing edges in a graph, based on HRG models.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.7.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_predict(const igraph_t *graph,
|
||
igraph_vector_int_t *edges,
|
||
igraph_vector_t *prob,
|
||
igraph_hrg_t *hrg,
|
||
igraph_bool_t start,
|
||
igraph_int_t num_samples,
|
||
igraph_int_t num_bins);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
Samples HRG models for a network, and estimated the probability
|
||
that an edge was falsely observed as non-existent in the network.
|
||
|
||
</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>edges</code></em>:</span></p></td>
|
||
<td><p>
|
||
The list of missing edges is stored here, the first
|
||
two elements are the first edge, the next two the second edge,
|
||
etc.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>prob</code></em>:</span></p></td>
|
||
<td><p>
|
||
Vector of probabilies for the existence of missing
|
||
edges, in the order corresponding to <code class="constant">edges</code>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
A HRG, it is used as a starting point if <code class="constant">start</code> is
|
||
true. It is also modified during the MCMC sampling.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>start</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to start the MCMC from the given HRG.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>num_samples</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of samples to generate.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>num_bins</code></em>:</span></p></td>
|
||
<td><p>
|
||
Controls the resolution of the edge
|
||
probabilities. Higher numbers result higher resolution.
|
||
</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: TODO.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="hrg-deprecated"></a>7. Deprecated functions</h2></div></div></div>
|
||
<div class="toc"><dl class="toc"><dt><span class="section"><a href="igraph-HRG.html#igraph_hrg_dendrogram">7.1. <code class="function">igraph_hrg_dendrogram</code> — Create a dendrogram from a hierarchical random graph.</a></span></dt></dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_hrg_dendrogram"></a>7.1. <code class="function">igraph_hrg_dendrogram</code> — Create a dendrogram from a hierarchical random graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.28.8.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_hrg_dendrogram(igraph_t *graph, const igraph_hrg_t *hrg);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
Creates the igraph graph equivalent of an <a class="link" href="igraph-HRG.html#igraph_hrg_t" title="2.1. igraph_hrg_t — Data structure to store a hierarchical random graph."><code class="function">igraph_hrg_t</code></a> data
|
||
structure.
|
||
|
||
</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 uninitialized graph, the result is
|
||
stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hrg</code></em>:</span></p></td>
|
||
<td><p>
|
||
The hierarchical random graph to convert.
|
||
</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), the number of vertices in the graph.
|
||
|
||
</p>
|
||
<div class="warning" style="margin-left: 0.5in; margin-right: 0.5in;">
|
||
<h3 class="title">Warning</h3>
|
||
<p>Deprecated since version 0.10.5. Please do not use this function in new
|
||
code; use <a class="link" href="igraph-HRG.html#igraph_from_hrg_dendrogram" title="5.1. igraph_from_hrg_dendrogram — Create a graph representation of the dendrogram of a hierarchical random graph model."><code class="function">igraph_from_hrg_dendrogram()</code></a>
|
||
instead.</p>
|
||
</div>
|
||
<p>
|
||
</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-Graphlets.html"><b>← Chapter 26. Graphlets</b></a></td>
|
||
<td align="right"><a accesskey="n" href="igraph-Embedding.html"><b>Chapter 28. Embedding of graphs →</b></a></td>
|
||
</tr></table>
|
||
</body>
|
||
</html>
|