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<html>
<head>
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<title>Chapter 3. Tutorial</title>
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<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">
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<div class="chapter">
<div class="titlepage"><div><div><h1 class="title">
<a name="igraph-Tutorial"></a>Chapter 3. Tutorial</h1></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1">1. Compiling programs using igraph</a></span></dt>
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-2">2. Creating your first graphs</a></span></dt>
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-3">3. Calculating various properties of graphs</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="tut-lesson-1"></a>1. Compiling programs using igraph</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-compiling-with-cmake">1.1. Compiling with CMake</a></span></dt>
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-compiling-without-cmake">1.2. Compiling without CMake</a></span></dt>
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-running-the-program">1.3. Running the program</a></span></dt>
</dl></div>
<p>
The following short example program demonstrates the basic usage of
the <span class="command"><strong>igraph</strong></span> library. Save it into a file named
<code class="filename">igraph_test.c</code>.
</p>
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> &lt;igraph.h&gt;
int <span class="strong"><strong>main</strong></span>(void) {
igraph_int_t num_vertices = 1000;
igraph_int_t num_edges = 1000;
igraph_real_t diameter, mean_degree;
igraph_t graph;
<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>();
<span class="emphasis"><em>/* Ensure identical results across runs. */</em></span>
<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_seed" title="3.3. igraph_rng_seed — Seeds a random number generator.">igraph_rng_seed</a></strong></span>(<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_default" title="2.1. igraph_rng_default — Query the default random number generator.">igraph_rng_default</a></strong></span>(), 42);
<span class="strong"><strong><a class="link" href="igraph-Games.html#igraph_erdos_renyi_game_gnm" title="1.1. igraph_erdos_renyi_game_gnm — Generates a random (Erdős-Rényi) graph with a fixed number of edges.">igraph_erdos_renyi_game_gnm</a></strong></span>(
&amp;graph, num_vertices, num_edges,
IGRAPH_UNDIRECTED, IGRAPH_SIMPLE_SW, IGRAPH_EDGE_UNLABELED);
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_diameter" title="3.22. igraph_diameter — Calculates the weighted diameter of a graph using Dijkstra's algorithm.">igraph_diameter</a></strong></span>(
&amp;graph, <span class="emphasis"><em>/* weights = */</em></span> NULL,
&amp;diameter,
<span class="emphasis"><em>/* from = */</em></span> NULL, <span class="emphasis"><em>/* to = */</em></span> NULL,
<span class="emphasis"><em>/* vertex_path = */</em></span> NULL, <span class="emphasis"><em>/* edge_path = */</em></span> NULL,
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* unconn= */</em></span> true);
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_mean_degree" title="26.2. igraph_mean_degree — The mean degree of a graph.">igraph_mean_degree</a></strong></span>(&amp;graph, &amp;mean_degree, IGRAPH_LOOPS);
<span class="strong"><strong>printf</strong></span>("Diameter of a random graph with average degree %g: %g\n",
mean_degree, diameter);
<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>(&amp;graph);
<span class="strong"><strong>return</strong></span> 0;
}
</pre>
<p>
</p>
<p>
This example illustrates a couple of points:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem"><p>
First, programs
using the <span class="command"><strong>igraph</strong></span> library should include the
<code class="filename">igraph.h</code> header
file. Note that while igraph installs several sub-headers, the organization of these may change
without notice. Only use <code class="filename">igraph.h</code> in your projects, not any of the sub-headers.
</p></li>
<li class="listitem"><p>
Second, the library must be initialized using
<a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library."><code class="function">igraph_setup()</code></a>
before use.
</p></li>
<li class="listitem"><p>
Third, <span class="command"><strong>igraph</strong></span> uses the
<span class="type">igraph_int_t</span> type for integers instead of
<span class="type">int</span> or <span class="type">long int</span>, and it also uses the
<span class="type">igraph_real_t</span> type for real numbers instead of
<span class="type">double</span>. Depending on how <span class="command"><strong>igraph</strong></span> was compiled, and whether you are
using a 32-bit or 64-bit system, <span class="type">igraph_int_t</span> may be a 32-bit
or 64-bit integer.
</p></li>
<li class="listitem"><p>
Fourth, <span class="command"><strong>igraph</strong></span> graph objects are represented by the <span class="type">igraph_t</span> data
type.
</p></li>
<li class="listitem"><p>
Fifth, the <a class="link" href="igraph-Games.html#igraph_erdos_renyi_game_gnm" title="1.1. igraph_erdos_renyi_game_gnm — Generates a random (Erdős-Rényi) graph with a fixed number of edges."><code class="function">igraph_erdos_renyi_game_gnm()</code></a>
creates a graph and <a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object."><code class="function">igraph_destroy()</code></a>
destroys it, i.e. deallocates the memory associated to it.
</p></li>
</ul></div>
<p>
For compiling this program you need a C compiler. Optionally,
<a class="ulink" href="https://cmake.org" target="_top">CMake</a> can be used to automate the compilation.
</p>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="tut-lesson-1-compiling-with-cmake"></a>1.1. Compiling with CMake</h3></div></div></div>
<p>
It is convenient to use CMake because it can automatically discover the
necessary compilation flags on all operating systems. Many IDEs support
CMake, and can work with CMake projects directly. To create a CMake project
for this example program, create a file name <code class="filename">CMakeLists.txt</code> with the
following contents:
</p>
<pre class="programlisting">
cmake_minimum_required(VERSION 3.18)
project(igraph_test)
find_package(igraph REQUIRED)
add_executable(igraph_test igraph_test.c)
target_link_libraries(igraph_test PUBLIC igraph::igraph)
</pre>
<p>
</p>
<p>
To compile the project, create a new directory called <code class="filename">build</code> in
the root of the <span class="command"><strong>igraph</strong></span> source tree, and switch to it:
</p>
<pre class="programlisting">
mkdir build
cd build
</pre>
<p>
</p>
<p>
Run CMake to configure the project:
</p>
<pre class="programlisting">
cmake ..
</pre>
<p>
</p>
<p>
If <span class="command"><strong>igraph</strong></span> was installed at a non-standard location, specify its prefix
using the <code class="option">-DCMAKE_PREFIX_PATH=...</code> option. The prefix must be
the same directory that was specified as the <code class="option">CMAKE_INSTALL_PREFIX</code>
when compiling igraph.
</p>
<p>
If configuration has succeeded, build the program using
</p>
<pre class="programlisting">
cmake --build .
</pre>
<p>
</p>
<div class="note" style="margin-left: 0.5in; margin-right: 0.5in;">
<h3 class="title">C++ must be enabled in igraph projects</h3>
<p>Parts of <span class="command"><strong>igraph</strong></span> are implemented in C++; therefore, any CMake target that
depends on <span class="command"><strong>igraph</strong></span> should use the C++ linker. Furthermore, OpenMP support in
igraph works correctly only if C++ is enabled in the CMake project. The script
that finds <span class="command"><strong>igraph</strong></span> on the host machine will throw an error if C++ support is
not enabled in the CMake project.</p>
<p>C++ support is enabled by default when no languages are explicitly
specified in CMake's <a class="ulink" href="https://cmake.org/cmake/help/latest/command/project.html" target="_top"><code class="code">project</code></a>
command, e.g. <code class="code">project(igraph_test)</code>. If you do specify some languages explicitly,
make sure to also include <code class="code">CXX</code>, e.g. <code class="code">project(igraph_test C CXX)</code>.
</p>
</div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="tut-lesson-1-compiling-without-cmake"></a>1.2. Compiling without CMake</h3></div></div></div>
<p>
On most Unix-like systems, the default C compiler is called <span class="command"><strong>cc</strong></span>.
To compile the test program, you will need a command similar to the following:
</p>
<pre class="programlisting">
cc igraph_test.c -I/usr/local/include/igraph -L/usr/local/lib -ligraph -o igraph_test
</pre>
<p>
</p>
<p>
The exact form depends on where <span class="command"><strong>igraph</strong></span> was installed on your
system, whether it was compiled as a shared or static library, and the external
libraries it was linked to. The directory after the <code class="option">-I</code> switch
is the one containing the <code class="filename">igraph.h</code> file, while the one
following <code class="option">-L</code> should contain the library file itself, usually a
file called <code class="filename">libigraph.a</code> (static library on macOS and
Linux), <code class="filename">libigraph.so</code> (shared library on Linux),
<code class="filename">libigraph.dylib</code> (shared library on macOS),
<code class="filename">igraph.lib</code> (static library on Windows) or
<code class="filename">igraph.dll</code> (shared library on Windows). If
<span class="command"><strong>igraph</strong></span> was compiled as a static library, it is also
necessary to manually link to all of its dependencies.
</p>
<p>
If your system has the <span class="command"><strong>pkg-config</strong></span> utility you are
likely to get the necessary compile options by issuing the command
</p>
<pre class="programlisting">
pkg-config --libs --cflags igraph
</pre>
<p>
(if <span class="command"><strong>igraph</strong></span> was built as a shared library) or
</p>
<pre class="programlisting">
pkg-config --static --libs --cflags igraph
</pre>
<p>
(if <span class="command"><strong>igraph</strong></span> was built as a static library).
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="tut-lesson-1-running-the-program"></a>1.3. Running the program</h3></div></div></div>
<p>
On most systems, the executable can be run by simply typing its name like this:
</p>
<pre class="programlisting">
./igraph_test
</pre>
<p>
If you use dynamic linking and the <span class="command"><strong>igraph</strong></span>
library is not installed in a standard place, you may need to add its location to the
<code class="envar">LD_LIBRARY_PATH</code> (Linux), <code class="envar">DYLD_LIBRARY_PATH</code> (macOS)
or <code class="envar">PATH</code> (Windows) environment variables. This is typically necessary
on Windows systems.
</p>
</div>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="tut-lesson-2"></a>2. Creating your first graphs</h2></div></div></div>
<p>
The functions generating graph objects are called graph
generators. Stochastic (i.e. randomized) graph generators are called
<span class="quote">“<span class="quote">games</span>”</span>.
</p>
<p>
<span class="command"><strong>igraph</strong></span> can handle directed and undirected graphs. Most graph
generators are able to create both types of graphs and most other
functions are usually also capable of handling
both. E.g., <a class="link" href="igraph-Structural.html#igraph_get_shortest_paths" title="3.8. igraph_get_shortest_paths — Shortest paths from a vertex."><code class="function">igraph_get_shortest_paths()</code></a>,
which calculates shortest paths from a vertex to other vertices, can calculate
directed or undirected paths.
</p>
<p>
<span class="command"><strong>igraph</strong></span> has sophisticated ways for creating graphs. The simplest
graphs are deterministic regular structures like star graphs
(<a class="link" href="igraph-Generators.html#igraph_star" title="4.1. igraph_star — Creates a star graph, every vertex connects only to the center."><code class="function">igraph_star()</code></a>),
cycle graphs (<a class="link" href="igraph-Generators.html#igraph_cycle_graph" title="4.9. igraph_cycle_graph — A cycle graph C_n."><code class="function">igraph_cycle_graph()</code></a>), lattices
(<a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices."><code class="function">igraph_square_lattice()</code></a>) or trees
(<a class="link" href="igraph-Generators.html#igraph_kary_tree" title="5.1. igraph_kary_tree — Creates a k-ary tree in which almost all vertices have k children."><code class="function">igraph_kary_tree()</code></a>), and many more.
</p>
<p>
The following example creates an undirected regular circular lattice,
adds some random edges to it and calculates the average length of
shortest paths between all pairs of vertices in the graph before and
after adding the random edges. (The message is that some random edges
can reduce path lengths a lot.)
</p>
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> &lt;igraph.h&gt;
int <span class="strong"><strong>main</strong></span>(void) {
igraph_t graph;
igraph_vector_int_t dimvector;
igraph_vector_int_t edges;
igraph_vector_bool_t periodic;
igraph_real_t avg_path_len;
<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>();
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&amp;dimvector, 2);
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(dimvector)[0] = 30;
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(dimvector)[1] = 30;
<span class="strong"><strong>igraph_vector_bool_init</strong></span>(&amp;periodic, 2);
<span class="strong"><strong>igraph_vector_bool_fill</strong></span>(&amp;periodic, true);
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices.">igraph_square_lattice</a></strong></span>(&amp;graph, &amp;dimvector, 0, IGRAPH_UNDIRECTED,
<span class="emphasis"><em>/* mutual= */</em></span> false, &amp;periodic);
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_average_path_length" title="3.20. igraph_average_path_length — The average shortest path length between all vertex pairs.">igraph_average_path_length</a></strong></span>(&amp;graph, NULL, &amp;avg_path_len, NULL,
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* unconn= */</em></span> true);
<span class="strong"><strong>printf</strong></span>("Average path length (lattice): %g\n", (double) avg_path_len);
<span class="emphasis"><em>/* Seed the RNG to ensure identical results across runs. */</em></span>
<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_seed" title="3.3. igraph_rng_seed — Seeds a random number generator.">igraph_rng_seed</a></strong></span>(<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_default" title="2.1. igraph_rng_default — Query the default random number generator.">igraph_rng_default</a></strong></span>(), 42);
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&amp;edges, 20);
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i &lt; <span class="strong"><strong>igraph_vector_int_size</strong></span>(&amp;edges); i++) {
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(edges)[i] = <span class="strong"><strong>RNG_INTEGER</strong></span>(0, <span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_vcount" title="5.2.1. igraph_vcount — The number of vertices in a graph.">igraph_vcount</a></strong></span>(&amp;graph) - 1);
}
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_add_edges" title="5.3.2. igraph_add_edges — Adds edges to a graph object.">igraph_add_edges</a></strong></span>(&amp;graph, &amp;edges, NULL);
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_average_path_length" title="3.20. igraph_average_path_length — The average shortest path length between all vertex pairs.">igraph_average_path_length</a></strong></span>(&amp;graph, NULL, &amp;avg_path_len, NULL,
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* unconn= */</em></span> true);
<span class="strong"><strong>printf</strong></span>("Average path length (randomized lattice): %g\n", (double) avg_path_len);
<span class="strong"><strong>igraph_vector_bool_destroy</strong></span>(&amp;periodic);
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&amp;dimvector);
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&amp;edges);
<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>(&amp;graph);
<span class="strong"><strong>return</strong></span> 0;
}
</pre>
<p>
</p>
<p>
This example illustrates some new points. <span class="command"><strong>igraph</strong></span> uses
<a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1.  About igraph_vector_t objects"><span class="type">igraph_vector_t</span></a>
and its related types (<span class="type">igraph_vector_int_t</span>, <span class="type">igraph_vector_bool_t</span>
and so on) instead of plain C arrays. <span class="type">igraph_vector_t</span> is superior to
regular arrays in almost every sense. Vectors are created by the
<a class="link" href="igraph-Data-structures.html#igraph_vector_init" title="2.2.1. igraph_vector_init — Initializes a vector object (constructor)."><code class="function">igraph_vector_init()</code></a>
function and, like graphs, they should be destroyed if not
needed any more by calling
<a class="link" href="igraph-Data-structures.html#igraph_vector_destroy" title="2.2.5. igraph_vector_destroy — Destroys a vector object."><code class="function">igraph_vector_destroy()</code></a>
on them. A vector can be indexed by the
<a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector."><code class="function">VECTOR()</code></a> function
(right now it is a macro). The elements of a vector are of type <span class="type">igraph_real_t</span>
for <a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1.  About igraph_vector_t objects"><span class="type">igraph_vector_t</span></a>,
and of type <span class="type">igraph_int_t</span> for <span class="type">igraph_vector_int_t</span>.
As you might expect, <span class="type">igraph_vector_bool_t</span> holds
<span class="type">igraph_bool_t</span> values. Vectors can be resized and most <span class="command"><strong>igraph</strong></span>
functions returning the result in a vector automatically resize it to the size they need.
</p>
<p>
<a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices."><code class="function">igraph_square_lattice()</code></a>
takes an integer vector argument specifying the dimensions of
the lattice. In this example we generate a 30x30 two dimensional
periodic lattice. See the documentation of
<a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices."><code class="function">igraph_square_lattice()</code></a> in
the reference manual for the other arguments.
</p>
<p>
The vertices in a graph are identified by a <span class="emphasis"><em>vertex ID</em></span>, an integer between
<code class="code">0</code> and <code class="code">n - 1</code>, where <code class="code">n</code> is the number of vertices in the graph.
The vertex count can be retrieved using <a class="link" href="igraph-Basic.html#igraph_vcount" title="5.2.1. igraph_vcount — The number of vertices in a graph."><code class="function">igraph_vcount()</code></a>,
as in the example.
</p>
<p>
The <a class="link" href="igraph-Basic.html#igraph_add_edges" title="5.3.2. igraph_add_edges — Adds edges to a graph object."><code class="function">igraph_add_edges()</code></a>
function simply takes a graph and a vector of
vertex IDs defining the new edges. The first edge is between the first
two vertex IDs in the vector, the second edge is between the second
two, etc. This way we add ten random edges to the lattice.
</p>
<p>
Note that this example program may add <span class="emphasis"><em>loop edges</em></span>, edges
pointing a vertex to itself, or <span class="emphasis"><em>multiple edges</em></span>, more than one edge
between the same pair of vertices.
<span class="type">igraph_t</span> can of course represent loops and multiple edges, although some
routines expect simple graphs, i.e. graphs which contain neither of these. This is because some
structural properties are ill-defined for non-simple graphs. Loop and multi-edges can be removed by calling
<a class="link" href="igraph-Operators.html#igraph_simplify" title="3.11. igraph_simplify — Removes loop and/or multiple edges from the graph."><code class="function">igraph_simplify()</code></a>.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="tut-lesson-3"></a>3. Calculating various properties of graphs</h2></div></div></div>
<p>
In our next example we will calculate various centrality measures in a
friendship graph. The friendship graph is from the famous Zachary karate
club study. (Do a web search on "Zachary karate" if you want to know more about
this.) Centrality measures quantify how central is the position of
individual vertices in the graph.
</p>
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> &lt;igraph.h&gt;
int <span class="strong"><strong>main</strong></span>(void) {
igraph_t graph;
igraph_vector_int_t result;
<a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1.  About igraph_vector_t objects">igraph_vector_t</a> result_real;
igraph_int_t edges_array[] = {
0,1, 0,2, 0,3, 0,4, 0,5, 0,6, 0,7, 0,8,
0,10, 0,11, 0,12, 0,13, 0,17, 0,19, 0,21, 0,31,
1, 2, 1, 3, 1, 7, 1,13, 1,17, 1,19, 1,21, 1,30,
2, 3, 2, 7, 2,27, 2,28, 2,32, 2, 9, 2, 8, 2,13,
3, 7, 3,12, 3,13, 4, 6, 4,10, 5, 6, 5,10, 5,16,
6,16, 8,30, 8,32, 8,33, 9,33, 13,33, 14,32, 14,33,
15,32, 15,33, 18,32, 18,33, 19,33, 20,32, 20,33,
22,32, 22,33, 23,25, 23,27, 23,32, 23,33, 23,29,
24,25, 24,27, 24,31, 25,31, 26,29, 26,33, 27,33,
28,31, 28,33, 29,32, 29,33, 30,32, 30,33, 31,32,
31,33, 32,33
};
igraph_vector_int_t edges =
<span class="strong"><strong>igraph_vector_int_view</strong></span>(edges_array, <span class="strong"><strong>sizeof</strong></span>(edges_array) / <span class="strong"><strong>sizeof</strong></span>(edges_array[0]));
<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>();
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_create" title="2.1. igraph_create — Creates a graph with the specified edges.">igraph_create</a></strong></span>(&amp;graph, &amp;edges, 0, IGRAPH_UNDIRECTED);
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&amp;result, 0);
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_init" title="2.2.1. igraph_vector_init — Initializes a vector object (constructor).">igraph_vector_init</a></strong></span>(&amp;result_real, 0);
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_degree" title="5.2.14. igraph_degree — The degree of some vertices in a graph.">igraph_degree</a></strong></span>(&amp;graph, &amp;result, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version).">igraph_vss_all</a></strong></span>(), IGRAPH_ALL, IGRAPH_LOOPS);
<span class="strong"><strong>printf</strong></span>("Maximum degree is %10" IGRAPH_PRId ", vertex %2" IGRAPH_PRId ".\n",
<span class="strong"><strong>igraph_vector_int_max</strong></span>(&amp;result),
<span class="strong"><strong>igraph_vector_int_which_max</strong></span>(&amp;result));
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_closeness" title="11.1. igraph_closeness — Closeness centrality calculations for some vertices.">igraph_closeness</a></strong></span>(&amp;graph, &amp;result_real, NULL, NULL, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version).">igraph_vss_all</a></strong></span>(),
IGRAPH_ALL, <span class="emphasis"><em>/* weights= */</em></span> NULL, <span class="emphasis"><em>/* normalized= */</em></span> false);
<span class="strong"><strong>printf</strong></span>("Maximum closeness is %10g, vertex %2" IGRAPH_PRId ".\n",
(double) <span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_max" title="2.10.2. igraph_vector_max — Largest element of a vector.">igraph_vector_max</a></strong></span>(&amp;result_real),
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_which_max" title="2.10.4. igraph_vector_which_max — Gives the index of the maximum element of the vector.">igraph_vector_which_max</a></strong></span>(&amp;result_real));
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_betweenness" title="11.3. igraph_betweenness — Betweenness centrality of some vertices.">igraph_betweenness</a></strong></span>(&amp;graph, <span class="emphasis"><em>/* weights= */</em></span> NULL, &amp;result_real, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version).">igraph_vss_all</a></strong></span>(),
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* normalized= */</em></span> false);
<span class="strong"><strong>printf</strong></span>("Maximum betweenness is %10g, vertex %2" IGRAPH_PRId ".\n",
(double) <span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_max" title="2.10.2. igraph_vector_max — Largest element of a vector.">igraph_vector_max</a></strong></span>(&amp;result_real),
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_which_max" title="2.10.4. igraph_vector_which_max — Gives the index of the maximum element of the vector.">igraph_vector_which_max</a></strong></span>(&amp;result_real));
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&amp;result);
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_destroy" title="2.2.5. igraph_vector_destroy — Destroys a vector object.">igraph_vector_destroy</a></strong></span>(&amp;result_real);
<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>(&amp;graph);
<span class="strong"><strong>return</strong></span> 0;
}
</pre>
<p>
</p>
<p>
This example demonstrates some new operations. First of all, it shows a
way to create a graph a list of edges stored in a plain C array.
Function <a class="link" href="igraph-Data-structures.html#igraph_vector_view" title="2.5.1. igraph_vector_view — Handle a regular C array as a igraph_vector_t."><code class="function">igraph_vector_view()</code></a>
creates a <span class="emphasis"><em>view</em></span> of a C array. It does not copy any data,
which means that you must not call
<a class="link" href="igraph-Data-structures.html#igraph_vector_destroy" title="2.2.5. igraph_vector_destroy — Destroys a vector object."><code class="function">igraph_vector_destroy()</code></a>
on a vector created this way. This vector is then used to create the
undirected graph.
</p>
<p>
Then the degree, closeness and betweenness centrality of the vertices
is calculated and the highest values are printed. Note that the vector
<code class="varname">result</code>, into which these functions will write their
result, must be initialized first, and also that the functions resize
it to be able to hold the result.
</p>
<p>
Notice that in order to print values of type <span class="type">igraph_int_t</span>,
we used the <code class="constant">IGRAPH_PRId</code> format macro constant. This
macro is similar to the standard <code class="constant">PRI</code> constants defined
in <code class="code">stdint.h</code>, and expands to the correct <code class="code">printf</code>
format specifier on each platform that <span class="command"><strong>igraph</strong></span> supports.
</p>
<p>
The <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> argument
tells the functions to calculate the property for every vertex in the graph.
It is shorthand for a <span class="emphasis"><em>vertex selector</em></span>, represented by type
<span class="type">igraph_vs_t</span>.
Vertex selectors help perform operations on a subset of vertices.
You can read more about them in <a class="link" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">one
of the following chapters</a>.
</p>
</div>
</div>
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