EVOLUTION-MANAGER
Edit File: centralize.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: Centralization of a graph</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 centralize {igraph}"><tr><td>centralize {igraph}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Centralization of a graph</h2> <h3>Description</h3> <p>Centralization is a method for creating a graph level centralization measure from the centrality scores of the vertices. </p> <h3>Usage</h3> <pre> centralize(scores, theoretical.max = 0, normalized = TRUE) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>scores</code></td> <td> <p>The vertex level centrality scores.</p> </td></tr> <tr valign="top"><td><code>theoretical.max</code></td> <td> <p>Real scalar. The graph-level centralization measure of the most centralized graph with the same number of vertices as the graph under study. This is only used if the <code>normalized</code> argument is set to <code>TRUE</code>.</p> </td></tr> <tr valign="top"><td><code>normalized</code></td> <td> <p>Logical scalar. Whether to normalize the graph level centrality score by dividing by the supplied theoretical maximum.</p> </td></tr> </table> <h3>Details</h3> <p>Centralization is a general method for calculating a graph-level centrality score based on node-level centrality measure. The formula for this is </p> <p style="text-align: center;"><i> C(G)=sum(max(c(w), w) - c(v), v),</i></p> <p>where <i>c(v)</i> is the centrality of vertex <i>v</i>. </p> <p>The graph-level centralization measure can be normalized by dividing by the maximum theoretical score for a graph with the same number of vertices, using the same parameters, e.g. directedness, whether we consider loop edges, etc. </p> <p>For degree, closeness and betweenness the most centralized structure is some version of the star graph, in-star, out-star or undirected star. </p> <p>For eigenvector centrality the most centralized structure is the graph with a single edge (and potentially many isolates). </p> <p><code>centralize</code> implements general centralization formula to calculate a graph-level score from vertex-level scores. </p> <h3>Value</h3> <p>A real scalar, the centralization of the graph from which <code>scores</code> were derived. </p> <h3>References</h3> <p>Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual Clarification. <em>Social Networks</em> 1, 215–239. </p> <p>Wasserman, S., and Faust, K. (1994). <em>Social Network Analysis: Methods and Applications.</em> Cambridge University Press. </p> <h3>See Also</h3> <p>Other centralization related: <code><a href="centr_betw_tmax.html">centr_betw_tmax</a>()</code>, <code><a href="centr_betw.html">centr_betw</a>()</code>, <code><a href="centr_clo_tmax.html">centr_clo_tmax</a>()</code>, <code><a href="centr_clo.html">centr_clo</a>()</code>, <code><a href="centr_degree_tmax.html">centr_degree_tmax</a>()</code>, <code><a href="centr_degree.html">centr_degree</a>()</code>, <code><a href="centr_eigen_tmax.html">centr_eigen_tmax</a>()</code>, <code><a href="centr_eigen.html">centr_eigen</a>()</code> </p> <h3>Examples</h3> <pre> # A BA graph is quite centralized g <- sample_pa(1000, m=4) centr_degree(g)$centralization centr_clo(g, mode="all")$centralization centr_eigen(g, directed=FALSE)$centralization # Calculate centralization from pre-computed scores deg <- degree(g) tmax <- centr_degree_tmax(g, loops=FALSE) centralize(deg, tmax) # The most centralized graph according to eigenvector centrality g0 <- graph( c(2,1), n=10, dir=FALSE ) g1 <- make_star(10, mode="undirected") centr_eigen(g0)$centralization centr_eigen(g1)$centralization </pre> <hr /><div style="text-align: center;">[Package <em>igraph</em> version 1.3.5 <a href="00Index.html">Index</a>]</div> </body></html>