Closeness centrality

[gmagerman]

Hi,

is the closeness centrality calculated here the mean of the geodesic paths or the inverse of that?
If it is the mean of the geodesic paths (as I might conclude from the short description), then having a low mean path length actually gives a node a low centrality value. So mostly, the inverse of this value is used.
Which one does Gephi calculate?
I think it would be great in general if Gephi would be able to provide standard equations and so for the calculations used

All the best!

[admin]

Hi,

We give it all here: https://wiki.gephi.org/index.php/Category:Measure

in particular: https://wiki.gephi.org/index.php/Closeness_Centrality

cheers

[gmagerman]

Dear Sebastien,

thanks for the info. However, there are some things that remain unclear from both the Gephi interface & the explanation given here.
- For eigenvector centrality in directed networks, which eigenvalues are used? left or right? In-centrality uses the right eigenvector, and vice versa.
- For closeness centrality, also directed versions exist, but the concepts are not given in the interface or the accompanying paper in the wiki.

In general, the HITS algorithm is an elegant alternative to these measures in directed networks, but when using eigvec centrality or close centrality in directed graphs, this should be clear to the user I guess...

- More fundamental, I think closeness centrality is expressed as explained in the UI (see attachment). But the reciprocal is more often used, since a high indegree stipulates a higher probability of being closer to everyone.



Ucinet and Mathematica provide values for both centralities above so it might be a useful addendum?

[shooter61]

I have the same problem. The short description implies that nodes with smaller closeness centrality are more closer to the rest of the network. However, in most of the other descriptions the closeness centrality is calculated with taking reciprocal of the total distances.

Does Eccentricity and Closeness values imply the same thing or opposite things?