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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: Kleinberg's authority centrality 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 authority_score {igraph}"><tr><td>authority_score {igraph}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Kleinberg's authority centrality scores.</h2> <h3>Description</h3> <p>The authority scores of the vertices are defined as the principal eigenvector of <i>t(A)*A</i>, where <i>A</i> is the adjacency matrix of the graph. </p> <h3>Usage</h3> <pre> authority_score(graph, scale = TRUE, weights = NULL, options = arpack_defaults) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>graph</code></td> <td> <p>The input graph.</p> </td></tr> <tr valign="top"><td><code>scale</code></td> <td> <p>Logical scalar, whether to scale the result to have a maximum score of one. If no scaling is used then the result vector has unit length in the Euclidean norm.</p> </td></tr> <tr valign="top"><td><code>weights</code></td> <td> <p>Optional positive weight vector for calculating weighted scores. If the graph has a <code>weight</code> edge attribute, then this is used by default. This function interprets edge weights as connection strengths. In the random surfer model, an edge with a larger weight is more likely to be selected by the surfer.</p> </td></tr> <tr valign="top"><td><code>options</code></td> <td> <p>A named list, to override some ARPACK options. See <code><a href="arpack.html">arpack</a></code> for details.</p> </td></tr> </table> <h3>Details</h3> <p>For undirected matrices the adjacency matrix is symmetric and the authority scores are the same as hub scores, see <code><a href="hub_score.html">hub_score</a></code>. </p> <h3>Value</h3> <p>A named list with members: </p> <table summary="R valueblock"> <tr valign="top"><td><code>vector</code></td> <td> <p>The authority/hub scores of the vertices.</p> </td></tr> <tr valign="top"><td><code>value</code></td> <td> <p>The corresponding eigenvalue of the calculated principal eigenvector.</p> </td></tr> <tr valign="top"><td><code>options</code></td> <td> <p>Some information about the ARPACK computation, it has the same members as the <code>options</code> member returned by <code><a href="arpack.html">arpack</a></code>, see that for documentation.</p> </td></tr> </table> <h3>References</h3> <p>J. Kleinberg. Authoritative sources in a hyperlinked environment. <em>Proc. 9th ACM-SIAM Symposium on Discrete Algorithms</em>, 1998. Extended version in <em>Journal of the ACM</em> 46(1999). Also appears as IBM Research Report RJ 10076, May 1997. </p> <h3>See Also</h3> <p><code><a href="hub_score.html">hub_score</a></code>, <code><a href="eigen_centrality.html">eigen_centrality</a></code> for eigenvector centrality, <code><a href="page_rank.html">page_rank</a></code> for the Page Rank scores. <code><a href="arpack.html">arpack</a></code> for the underlining machinery of the computation. </p> <h3>Examples</h3> <pre> ## An in-star g <- make_star(10) hub_score(g)$vector authority_score(g)$vector ## A ring g2 <- make_ring(10) hub_score(g2)$vector authority_score(g2)$vector </pre> <hr /><div style="text-align: center;">[Package <em>igraph</em> version 1.3.5 <a href="00Index.html">Index</a>]</div> </body></html>