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graph-algorithmgephi

Graph Closeness - Different result with gephi and NodeXL

I'm writing a JavaScript library for calculating graph measurements such as degree centrality, eccentrality, closeness and betweenness.

In order to validate my library I use two exist applications Gephi and NodeXL to run calculation with them. The problem is I got what looks like different results.

I build simple graph:

  (A) ----- (B)
   |         |
   |         | 
  (C) ----- (D)

Gephi gave those results:

A ecc=2 close=1.333 bet=0.5
B ecc=2 close=1.333 bet=0.5
C ecc=2 close=1.333 bet=0.5
D ecc=2 close=1.333 bet=0.5

NodeXL gave those results:

A close=0.25 bet=0.5
B close=0.25 bet=0.5
C close=0.25 bet=0.5
D close=0.25 bet=0.5

Note that NodeXL does not calculate eccentrality.

Which one is right?
Are the results really different?

I didn't normalize (or at least not intend to normalize) any results.

Solution

  • It seems that Gephi returns the average sum of all shortest paths between a node and all other nodes in the network (also stated in the doc) for A this gives: (1 + 1 + 2)/3=1.333333

    while NodeXL gives you the inverse sum of all shortest paths: for A 1/(1+1+2)=0.25

    So, I'd say the later is correct, as this is following the definition of closeness centrality. E.g. igraph also uses the second version.