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<!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: Find Bonacich alpha centrality scores of network positions</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 alpha_centrality {igraph}"><tr><td>alpha_centrality {igraph}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Find Bonacich alpha centrality scores of network positions</h2> <h3>Description</h3> <p><code>alpha_centrality</code> calculates the alpha centrality of some (or all) vertices in a graph. </p> <h3>Usage</h3> <pre> alpha_centrality( graph, nodes = V(graph), alpha = 1, loops = FALSE, exo = 1, weights = NULL, tol = 1e-07, sparse = TRUE ) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>graph</code></td> <td> <p>The input graph, can be directed or undirected</p> </td></tr> <tr valign="top"><td><code>nodes</code></td> <td> <p>Vertex sequence, the vertices for which the alpha centrality values are returned. (For technical reasons they will be calculated for all vertices, anyway.)</p> </td></tr> <tr valign="top"><td><code>alpha</code></td> <td> <p>Parameter specifying the relative importance of endogenous versus exogenous factors in the determination of centrality. See details below.</p> </td></tr> <tr valign="top"><td><code>loops</code></td> <td> <p>Whether to eliminate loop edges from the graph before the calculation.</p> </td></tr> <tr valign="top"><td><code>exo</code></td> <td> <p>The exogenous factors, in most cases this is either a constant – the same factor for every node, or a vector giving the factor for every vertex. Note that too long vectors will be truncated and too short vectors will be replicated to match the number of vertices.</p> </td></tr> <tr valign="top"><td><code>weights</code></td> <td> <p>A character scalar that gives the name of the edge attribute to use in the adjacency matrix. If it is <code>NULL</code>, then the ‘weight’ edge attribute of the graph is used, if there is one. Otherwise, or if it is <code>NA</code>, then the calculation uses the standard adjacency matrix.</p> </td></tr> <tr valign="top"><td><code>tol</code></td> <td> <p>Tolerance for near-singularities during matrix inversion, see <code><a href="../../Matrix/html/solve-methods.html">solve</a></code>.</p> </td></tr> <tr valign="top"><td><code>sparse</code></td> <td> <p>Logical scalar, whether to use sparse matrices for the calculation. The ‘Matrix’ package is required for sparse matrix support</p> </td></tr> </table> <h3>Details</h3> <p>The alpha centrality measure can be considered as a generalization of eigenvector centerality to directed graphs. It was proposed by Bonacich in 2001 (see reference below). </p> <p>The alpha centrality of the vertices in a graph is defined as the solution of the following matrix equation: </p> <p style="text-align: center;"><i>x=alpha t(A)x+e,</i></p> <p>where <i>A</i> is the (not necessarily symmetric) adjacency matrix of the graph, <i>e</i> is the vector of exogenous sources of status of the vertices and <i>alpha</i> is the relative importance of the endogenous versus exogenous factors. </p> <h3>Value</h3> <p>A numeric vector contaning the centrality scores for the selected vertices. </p> <h3>Warning</h3> <p>Singular adjacency matrices cause problems for this algorithm, the routine may fail is certain cases. </p> <h3>Author(s)</h3> <p>Gabor Csardi <a href="mailto:csardi.gabor@gmail.com">csardi.gabor@gmail.com</a> </p> <h3>References</h3> <p>Bonacich, P. and Lloyd, P. (2001). “Eigenvector-like measures of centrality for asymmetric relations” <em>Social Networks</em>, 23, 191-201. </p> <h3>See Also</h3> <p><code><a href="eigen_centrality.html">eigen_centrality</a></code> and <code><a href="power_centrality.html">power_centrality</a></code> </p> <h3>Examples</h3> <pre> # The examples from Bonacich's paper g.1 <- graph( c(1,3,2,3,3,4,4,5) ) g.2 <- graph( c(2,1,3,1,4,1,5,1) ) g.3 <- graph( c(1,2,2,3,3,4,4,1,5,1) ) alpha_centrality(g.1) alpha_centrality(g.2) alpha_centrality(g.3,alpha=0.5) </pre> <hr /><div style="text-align: center;">[Package <em>igraph</em> version 1.3.5 <a href="00Index.html">Index</a>]</div> </body></html>