Eigenvector Centrality Values Especially Low?

Mar 31, 2012 at 9:01 PM

I had a question about Eigenvector Centrality. I'm creating a network of approx. 100 vertices and 800 total ties to demonstrate collaborations between medical faculty and community organizations. I tried to show vertex size as a measure of Eigenvector Centrality, and have the newest NodeXL so had the program show the "top" values for me. The top values are around 0.018 and I wondered why those numbers are so low. As more info, some of the vertices are actually duplicates because some faculty members are also listed as "collaborative" individuals; I wonder if this helps explain the low figures? Any help in understanding how the numerical values are calculated is helpful, and thank you in advance!

Mar 31, 2012 at 9:11 PM

Also, one other point: the data in this collaboration network was based on survey responses that faculty filled out. All ties are by nature collaborative, so I did not enter in multiple ties (e.g. A -> B AND B ->A) but rather just the survey responder (A) and the collaborative individual/organization (B). Thus, I only entered A -> B. Could this explain the low Eigenvector values?

Apr 2, 2012 at 2:47 AM

also, here is a link to the basic excel data i used for the network (connections simply placed in two columns, similar to the layout in nodexl). perhaps it might help to look at the basic connections in order to see why the eigenvector values are low (i think you need to add the .xls extension post-download). 

http://dl.dropbox.com/u/169398/Basic%20Connections_3.20.12

Apr 2, 2012 at 4:11 PM

Hello, Ross:

I don't know the answer to your question.   To calculate eigenvector centrality, as well as a number of other graph metrics, NodeXL uses a graph library called SNAP, which is from Jure Leskovec's group at Stanford University.  NodeXL does this because SNAP was written by some graph metric experts (which I am not) and is very fast.

You might try contacting Jure with your question.  However, I would make the question more specific, as I am not sure whether you are questioning the accuracy of the eigenvector metrics in your particular graph, or you are looking for a pointer to the specific algorithm used to calculate eigenvector centrality, or you are wondering what eigenvector centrality is all about in general.

Jure can be reached via the People link at http://snap.stanford.edu/index.html.

-- Tony

Apr 2, 2012 at 5:06 PM

Thank you Tony. I'll go ahead and contact Jure and see if I can be more specific with my inquiry. I appreciate your comment.

 

Ross