Eigenvector centrality - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T06:41:41Z http://mathoverflow.net/feeds/question/32645 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/32645/eigenvector-centrality Eigenvector centrality Spencer 2010-07-20T14:40:06Z 2010-09-14T19:22:16Z <p>I was wondering if you can calculate eigenvector centrality with undirected graphs and if you can, what is the best means of doing so. I understand how to calculate the adjacency matrix and how to calculate its eigenvector (spectral) decomposition, I just am unaware as to how to combine this parts in order to calculate eigenvector centrality. Thanks in advance!</p> http://mathoverflow.net/questions/32645/eigenvector-centrality/35891#35891 Answer by douglas-klein for Eigenvector centrality douglas-klein 2010-08-17T17:46:10Z 2010-08-17T17:46:10Z <p>The wikipedia article quoted by Jon Bannon mentions using the power-iteration method as readily applicable -- and this is in my experience (for connected graphs, with degrees &lt;5)quite efficient, say starting with the vector with weight 1 for every site. And this wikipedia article mentions several other choices for measuring centrality, besides the "eigenvector centrality". But it does not mention some choices indicated in D. J. Klein, "Centrality Measure in Graphs", J. Math. Chem. 47 (2010) 1209-1223. There centrality measure is suggested to be related to choice of metric or semimetric D on the graph. A couple choices for D yield centrality measures very similar to common measures, and a new "resistive centrality" is noted to result in connection with the choice of D as the "resistance distance" metric. </p>