Closeness and eigenvector centrality for directed graphs

Computing metrics, community detection and data handling
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Zapata
Posts: 5
Joined: 20 Feb 2017 15:11

Closeness and eigenvector centrality for directed graphs

Post by Zapata » 01 Mar 2017 14:07

Hi all,

does anyone know how the closeness centrality and eigenvector centrality metrics are calculated for a directed graph? Is it based on "sending" (outdegree) or "receiving" (indegree) connections?

The Github page (https://github.com/gephi/gephi/wiki/Clo ... Centrality) does not help here unfortunately.

Kind regards,
Stefan

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eduramiba
Gephi Code Manager
Posts: 920
Joined: 22 Mar 2010 15:30
Location: Madrid, Spain

Re: Closeness and eigenvector centrality for directed graphs

Post by eduramiba » 01 Mar 2017 15:55

Hi,
Not sure now but you can check the code here: https://github.com/gephi/gephi/blob/mas ... tance.java

Zapata
Posts: 5
Joined: 20 Feb 2017 15:11

Re: Closeness and eigenvector centrality for directed graphs

Post by Zapata » 01 Mar 2017 16:47

Thanks.

I built a small test model and found the answers:

Closeness centrality of node A is based on the shortest path from A to other nodes in the network
Eigenvector centrality of node A is based on the importance of nodes (not sure which metric is used for importance) that supply into A, into A's supplier etc.

Overall, these definitions are surprising as closeness centrality will be correlated to outdegree whereas eigenvector centrality will be correlated to indegree. Not sure if that makes sense - any views on that?

AJS2017
Posts: 1
Joined: 24 May 2017 23:23

Re: Closeness and eigenvector centrality for directed graphs

Post by AJS2017 » 24 May 2017 23:28

Dear all,

Thanks for your contribution. I needed this for a project I am doing. I also checked the eigenvector centrality in Gephi. @Zapata as right. eigenvector centrality is correlated with indegree. It does make sense as it is indeed how eigenvector centrality is calculated by other softwares. However, answers given by other softwares are not the same for my dataset. I am using MIT network programmes here http://strategic.mit.edu/downloads.php? ... b_networks

In my case, this eigenvector centrality is the popularity sore of nodes in my data: flows going into the nodes by weight. Hope this helps.

Regards,
AJS

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