EVOLUTION-MANAGER
Edit File: sample_fitness_pl.html
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Scale-free random graphs, from vertex fitness scores</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for sample_fitness_pl {igraph}"><tr><td>sample_fitness_pl {igraph}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Scale-free random graphs, from vertex fitness scores</h2> <h3>Description</h3> <p>This function generates a non-growing random graph with expected power-law degree distributions. </p> <h3>Usage</h3> <pre> sample_fitness_pl( no.of.nodes, no.of.edges, exponent.out, exponent.in = -1, loops = FALSE, multiple = FALSE, finite.size.correction = TRUE ) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>no.of.nodes</code></td> <td> <p>The number of vertices in the generated graph.</p> </td></tr> <tr valign="top"><td><code>no.of.edges</code></td> <td> <p>The number of edges in the generated graph.</p> </td></tr> <tr valign="top"><td><code>exponent.out</code></td> <td> <p>Numeric scalar, the power law exponent of the degree distribution. For directed graphs, this specifies the exponent of the out-degree distribution. It must be greater than or equal to 2. If you pass <code>Inf</code> here, you will get back an Erdos-Renyi random network.</p> </td></tr> <tr valign="top"><td><code>exponent.in</code></td> <td> <p>Numeric scalar. If negative, the generated graph will be undirected. If greater than or equal to 2, this argument specifies the exponent of the in-degree distribution. If non-negative but less than 2, an error will be generated.</p> </td></tr> <tr valign="top"><td><code>loops</code></td> <td> <p>Logical scalar, whether to allow loop edges in the generated graph.</p> </td></tr> <tr valign="top"><td><code>multiple</code></td> <td> <p>Logical scalar, whether to allow multiple edges in the generated graph.</p> </td></tr> <tr valign="top"><td><code>finite.size.correction</code></td> <td> <p>Logical scalar, whether to use the proposed finite size correction of Cho et al., see references below.</p> </td></tr> </table> <h3>Details</h3> <p>This game generates a directed or undirected random graph where the degrees of vertices follow power-law distributions with prescribed exponents. For directed graphs, the exponents of the in- and out-degree distributions may be specified separately. </p> <p>The game simply uses <code><a href="sample_fitness.html">sample_fitness</a></code> with appropriately constructed fitness vectors. In particular, the fitness of vertex <i>i</i> is <i>i^(-alpha)</i>, where <i>alpha = 1/(gamma-1)</i> and gamma is the exponent given in the arguments. </p> <p>To remove correlations between in- and out-degrees in case of directed graphs, the in-fitness vector will be shuffled after it has been set up and before <code><a href="sample_fitness.html">sample_fitness</a></code> is called. </p> <p>Note that significant finite size effects may be observed for exponents smaller than 3 in the original formulation of the game. This function provides an argument that lets you remove the finite size effects by assuming that the fitness of vertex <i>i</i> is <i>(i+i0-1)^(-alpha)</i> where <i>i0</i> is a constant chosen appropriately to ensure that the maximum degree is less than the square root of the number of edges times the average degree; see the paper of Chung and Lu, and Cho et al for more details. </p> <h3>Value</h3> <p>An igraph graph, directed or undirected. </p> <h3>Author(s)</h3> <p>Tamas Nepusz <a href="mailto:ntamas@gmail.com">ntamas@gmail.com</a> </p> <h3>References</h3> <p>Goh K-I, Kahng B, Kim D: Universal behaviour of load distribution in scale-free networks. <em>Phys Rev Lett</em> 87(27):278701, 2001. </p> <p>Chung F and Lu L: Connected components in a random graph with given degree sequences. <em>Annals of Combinatorics</em> 6, 125-145, 2002. </p> <p>Cho YS, Kim JS, Park J, Kahng B, Kim D: Percolation transitions in scale-free networks under the Achlioptas process. <em>Phys Rev Lett</em> 103:135702, 2009. </p> <h3>Examples</h3> <pre> g <- sample_fitness_pl(10000, 30000, 2.2, 2.3) ## Not run: plot(degree_distribution(g, cumulative=TRUE, mode="out"), log="xy") </pre> <hr /><div style="text-align: center;">[Package <em>igraph</em> version 1.3.5 <a href="00Index.html">Index</a>]</div> </body></html>