Eigenvector centrality

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Eigenvector centrality

Hi,

I am new to programming and I am trying to calculate the eigenvector centrality of an directed graph mapping onto a social network. These are large matrices. I know how to calculate eigenvectors and the adjacency matrix associated with the graph. I am just unsure how to combine those two parts to calculate eigenvector centrality. Thanks in advance.

-Spencer

+1 A:

Say you have the nxn adjacency matrix for your graph of n nodes. Then you will need to calculate the eigenvector of this matrix associated with the largest eigenvalue. The centrality of the ith node is given by the ith element of this normalized eigenvector.
See http://113.212.161.150/elibrary/Library/Social_Network/Bonacich_Some.pdf and http://www.jstor.org/stable/2780000 for more background.

Larry Wang 2010-07-19 20:50:42

This is actually how I was previously calculating eigenvalue centrality. However, for directed graphs that were not symmetric this formula was returning non-real eigenvectors. Is this unavoidable? Can you not calculate EVC for directed unsymmetrical graphs?

Spencer 2010-07-19 21:17:33

I would guess that eigenvector centrality may not be an appropriate measure for such graphs, but I am far from an expert in this area. You may get better results reposting this question on [mathoverflow.net](http://mathoverflow.net/) with a `graph-theory` tag.

Larry Wang 2010-07-19 22:00:56

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