Add graph references
This commit is contained in:
Abdelrahman Said
@@ -0,0 +1,274 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||||
<title>Chapter 30. Processes on 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-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="next" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<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-Layout.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-Foreign.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-Processes"></a>Chapter 30. Processes on graphs</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc"><dt><span class="section"><a href="igraph-Processes.html#epidemic-models">1. Epidemic models</a></span></dt></dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="epidemic-models"></a>1. Epidemic models</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Processes.html#igraph_sir">1.1. <code class="function">igraph_sir</code> — Performs a number of SIR epidemics model runs on a graph.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Processes.html#igraph_sir_t">1.2. <code class="function">igraph_sir_t</code> — The result of one SIR model simulation.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Processes.html#igraph_sir_destroy">1.3. <code class="function">igraph_sir_destroy</code> — Deallocates memory associated with a SIR simulation run.</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_sir"></a>1.1. <code class="function">igraph_sir</code> — Performs a number of SIR epidemics model runs on a graph.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.31.2.2.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_sir(const igraph_t *graph, igraph_real_t beta,
|
||||
igraph_real_t gamma, igraph_int_t no_sim,
|
||||
igraph_vector_ptr_t *result);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
The SIR model is a simple model from epidemiology. The individuals
|
||||
of the population might be in three states: susceptible, infected
|
||||
and recovered. Recovered people are assumed to be immune to the
|
||||
disease. Susceptibles become infected with a rate that depends on
|
||||
their number of infected neighbors. Infected people become recovered
|
||||
with a constant rate. See these parameters below.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
This function runs multiple simulations, all starting with a
|
||||
single uniformly randomly chosen infected individual. A simulation
|
||||
is stopped when no infected individuals are left.
|
||||
|
||||
</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 perform the model on. For directed graphs
|
||||
edge directions are ignored and a warning is given.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>beta</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The rate of infection of an individual that is
|
||||
susceptible and has a single infected neighbor.
|
||||
The infection rate of a susceptible individual with n
|
||||
infected neighbors is n times beta. Formally
|
||||
this is the rate parameter of an exponential distribution.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>gamma</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The rate of recovery of an infected individual.
|
||||
Formally, this is the rate parameter of an exponential
|
||||
distribution.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>no_sim</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The number of simulation runs to perform.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>result</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The result of the simulation is stored here,
|
||||
in a list of <a class="link" href="igraph-Processes.html#igraph_sir_t" title="1.2. igraph_sir_t — The result of one SIR model simulation."><code class="function">igraph_sir_t</code></a> objects. To deallocate
|
||||
memory, the user needs to call <a class="link" href="igraph-Processes.html#igraph_sir_destroy" title="1.3. igraph_sir_destroy — Deallocates memory associated with a SIR simulation run."><code class="function">igraph_sir_destroy</code></a> on
|
||||
each element, before destroying the pointer vector itself
|
||||
using <a class="link" href="igraph-Data-structures.html#igraph_vector_ptr_destroy_all" title="2.17.5. igraph_vector_ptr_destroy_all — Frees all the elements and destroys the pointer vector."><code class="function">igraph_vector_ptr_destroy_all()</code></a>.
|
||||
</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(no_sim * (|V| + |E| log(|V|))).
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_sir_t"></a>1.2. <code class="function">igraph_sir_t</code> — The result of one SIR model simulation.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.31.2.3.2"></a><p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
typedef struct igraph_sir_t {
|
||||
igraph_vector_t times;
|
||||
igraph_vector_int_t no_s, no_i, no_r;
|
||||
} igraph_sir_t;
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
</p>
|
||||
<p>Data structure to store the results of one simulation
|
||||
of the SIR (susceptible-infected-recovered) model on a graph.
|
||||
|
||||
It has the following members. They are all (real or integer)
|
||||
vectors, and they are of the same length.
|
||||
|
||||
</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">times</code>:</span></p></td>
|
||||
<td><p>
|
||||
A vector, the times of the events are stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">no_s</code>:</span></p></td>
|
||||
<td><p>
|
||||
An integer vector, the number of susceptibles in
|
||||
each time step is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">no_i</code>:</span></p></td>
|
||||
<td><p>
|
||||
An integer vector, the number of infected individuals
|
||||
at each time step, is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">no_r</code>:</span></p></td>
|
||||
<td><p>
|
||||
An integer vector, the number of recovered individuals
|
||||
is stored here at each time step.</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_sir_destroy"></a>1.3. <code class="function">igraph_sir_destroy</code> — Deallocates memory associated with a SIR simulation run.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.31.2.4.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
void igraph_sir_destroy(igraph_sir_t *sir);
|
||||
</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>sir</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The <a class="link" href="igraph-Processes.html#igraph_sir_t" title="1.2. igraph_sir_t — The result of one SIR model simulation."><code class="function">igraph_sir_t</code></a> object storing the simulation.</p></td>
|
||||
</tr></tbody>
|
||||
</table></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-Layout.html"><b>← Chapter 29. Generating layouts for graph drawing</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Foreign.html"><b>Chapter 31. Reading and writing graphs from and to files →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user