EVOLUTION-MANAGER
Edit File: constraint.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: Burt's constraint</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 constraint {igraph}"><tr><td>constraint {igraph}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Burt's constraint</h2> <h3>Description</h3> <p>Given a graph, <code>constraint</code> calculates Burt's constraint for each vertex. </p> <h3>Usage</h3> <pre> constraint(graph, nodes = V(graph), weights = NULL) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>graph</code></td> <td> <p>A graph object, the input graph.</p> </td></tr> <tr valign="top"><td><code>nodes</code></td> <td> <p>The vertices for which the constraint will be calculated. Defaults to all vertices.</p> </td></tr> <tr valign="top"><td><code>weights</code></td> <td> <p>The weights of the edges. If this is <code>NULL</code> and there is a <code>weight</code> edge attribute this is used. If there is no such edge attribute all edges will have the same weight.</p> </td></tr> </table> <h3>Details</h3> <p>Burt's constraint is higher if ego has less, or mutually stronger related (i.e. more redundant) contacts. Burt's measure of constraint, <i>C[i]</i>, of vertex <i>i</i>'s ego network <i>V[i]</i>, is defined for directed and valued graphs, </p> <p style="text-align: center;"><i> C[i] = sum( [sum( p[i,j] + p[i,q] p[q,j], q in V[i], q != i,j )]^2, j in V[i], j != i). </i></p> <p>for a graph of order (ie. number of vertices) <i>N</i>, where proportional tie strengths are defined as </p> <p style="text-align: center;"><i> p[i,j]=(a[i,j]+a[j,i]) / sum(a[i,k]+a[k,i], k in V[i], k != i), </i></p> <p><i>a[i,j]</i> are elements of <i>A</i> and the latter being the graph adjacency matrix. For isolated vertices, constraint is undefined. </p> <h3>Value</h3> <p>A numeric vector of constraint scores </p> <h3>Author(s)</h3> <p>Jeroen Bruggeman (<a href="https://sites.google.com/site/jebrug/jeroen-bruggeman-social-science">https://sites.google.com/site/jebrug/jeroen-bruggeman-social-science</a>) and Gabor Csardi <a href="mailto:csardi.gabor@gmail.com">csardi.gabor@gmail.com</a> </p> <h3>References</h3> <p>Burt, R.S. (2004). Structural holes and good ideas. <em>American Journal of Sociology</em> 110, 349-399. </p> <h3>Examples</h3> <pre> g <- sample_gnp(20, 5/20) constraint(g) </pre> <hr /><div style="text-align: center;">[Package <em>igraph</em> version 1.3.5 <a href="00Index.html">Index</a>]</div> </body></html>