Strange Eigenvector Centrality Values
I have a simple graph with a few components (less than 30 nodes in total). When I calculate a simple eigenvector centrality measure (as in the documentation), x[0] = inf and all the values in x[1].a = 06666667. I was wondering whether I'm missing something or if there is an explanation for why this is the case? Thank you! -- View this message in context: http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/... Sent from the Main discussion list for the graph-tool project mailing list archive at Nabble.com.
On 09/29/2012 07:27 PM, cc wrote:
I have a simple graph with a few components (less than 30 nodes in total). When I calculate a simple eigenvector centrality measure (as in the documentation), x[0] = inf and all the values in x[1].a = 06666667. I was wondering whether I'm missing something or if there is an explanation for why this is the case? Thank you!
Could you please provide a graph where this problem occurs? Cheers, Tiago -- Tiago de Paula Peixoto <tiago@skewed.de>
Graph in GraphML <http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/file/n4024784/example_graph.graphml> Graph in PDF <http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/file/n4024784/example_graph.pdf> Hi, thank you for the reply. Attached are two files: a graph in GraphML format, and a PDF of the graph. It's a very simple graph, but similar to what I described. In this case x[1].a = 0.03571429 and x[0] = inf. -- View this message in context: http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/... Sent from the Main discussion list for the graph-tool project mailing list archive at Nabble.com.
Hi, On 09/29/2012 08:58 PM, cc wrote:
Graph in GraphML <http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/file/n4024784/example_graph.graphml> Graph in PDF <http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/file/n4024784/example_graph.pdf>
Hi, thank you for the reply. Attached are two files: a graph in GraphML format, and a PDF of the graph. It's a very simple graph, but similar to what I described. In this case x[1].a = 0.03571429 and x[0] = inf.
Yes, it is a bug with undirected graphs... I have just fixed it in the git version. Thanks for reporting this! Cheers, Tiago -- Tiago de Paula Peixoto <tiago@skewed.de>
Great, glad I could have helped! Before I jump to the git version, I'm curious as to whether graph-tool can calculate eigenvector centrality for signed networks. Bonacich and Lloyd suggest a eigenvector measure on a symmetrical adjacency matrix to infer status (2004) <http://www.sciencedirect.com/science/article/pii/S0378873304000449> . That is to say, an edge signed with -1 represents a negative relationship, and an edge signed with 1 represents a positive relationship, and thus those with negative and positive eigenvector centralities belong in different "cliques". Is it possible to arrive at this idea through the eigenvector centrality implemented in graph-tool if one were to assign -1 or 1 as edge weights in the graph? I.e., does the implemented algorithm take into account negative vs. positive weights? Sorry to jump the gun here, but the extensibility of graph-tool to more obscure measures is intriguing... -- View this message in context: http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/... Sent from the Main discussion list for the graph-tool project mailing list archive at Nabble.com.
On 09/29/2012 09:22 PM, cc wrote:
Great, glad I could have helped! Before I jump to the git version, I'm curious as to whether graph-tool can calculate eigenvector centrality for signed networks. Bonacich and Lloyd suggest a eigenvector measure on a symmetrical adjacency matrix to infer status (2004) <http://www.sciencedirect.com/science/article/pii/S0378873304000449> . That is to say, an edge signed with -1 represents a negative relationship, and an edge signed with 1 represents a positive relationship, and thus those with negative and positive eigenvector centralities belong in different "cliques". Is it possible to arrive at this idea through the eigenvector centrality implemented in graph-tool if one were to assign -1 or 1 as edge weights in the graph? I.e., does the implemented algorithm take into account negative vs. positive weights? Sorry to jump the gun here, but the extensibility of graph-tool to more obscure measures is intriguing...
This should work without a problem. The function in graph-tool implements the power method, which works for any matrix, and always converges as long as the largest eigenvalue is non-degenerate. Cheers, Tiago -- Tiago de Paula Peixoto <tiago@skewed.de>
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