Metrics! Eigenvector centrality and closeness centrality

Coordinator
Feb 17, 2009 at 5:34 AM
Edited Feb 17, 2009 at 5:35 AM
Many people have asked the NodeXL team for additional metrics for networks.  In the latest release we provide two new measures for your networks: Eigenvector Centrality and Closeness Centrality!

We would like to hear from you about additional measures that are of high priority in your work.
 
1.0.1.74
(2009/2/13)
  • Eigenvector centrality was added to the list of available graph metrics, which is accessible by going to NodeXL, Analysis in the Excel ribbon and clicking the down-arrow to the right of the Calculate Graph Metrics button. Eigenvector centrality is defined at http://en.wikipedia.org/wiki/Eigenvector_centrality#eigenvector_centrality. The accelerated power method is used to obtain the dominant eigenvector.
  • Closeness centrality was also added to the list. The closeness centrality of a vertex is the mean geodesic distance (shortest path) between it and all other vertices reachable from it. Closeness centrality defined.

More to come from Team NodeXL!

Feb 22, 2009 at 7:23 PM
The addition of the centrality measures is very useful for me.  I'm wondering, is it possible to plot vertecies on my graph so that nodes with higher centrality scores are closer to the center of the graph?
Feb 22, 2009 at 10:20 PM
I very much like jnvictor's idea.  It would be useful to me, too--as an option.
Feb 25, 2009 at 3:08 PM
That is not possible today.  However, we have a "radial layout" feature on our list of work items.  The radial layout will use a new pair of columns, called something like Theta and R, which will specify each node's position in a polar coordinate space.  You could then use NodeXL's AutoFill Columns feature to automatically fill the R column based on any calculated metric, including the centrality metrics.  The vertices with a high centrality metric would then be clustered at the center of the graph.

-- Tony
Feb 28, 2009 at 9:33 PM

Great work, thanks guys.

A novice question about eigenvector centrality: the wikipedia reference you give suggests that the centrality measure depends on a per-node score. However, that score seems to be an input that can be defined in any number of ways. How did you determine the score of a node?

Mar 2, 2009 at 4:02 PM
The scores are determined as a set.  The set of scores must satisfy two conditions:

1. They solve the eigenvector equation given in the Wikipedia article.

2. The largest eigenvalue is used in the same equation.

The largest eigenvalue is computed using an algorithm known as the accelerated power method.  The clearest explanation I found for this algorithm can be found here:

http://www.analytictech.com/networks/centaids.htm

-- Tony