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=0.5B ecc=2 close=1.333 bet=0.5C ecc=2 close=1.333 bet=0.5D ecc=2 close=1.333 bet=0.5NodeXL gave those results:A close=0.25 bet=0.5B close=0.25 bet=0.5C close=0.25 bet=0.5D close=0.25 bet=0.5Note 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.
Graph Closeness - Different result with gephi and NodeXL
graph theory;terminology;graphs
The closeness of a node in a graph is defined as the reciprocal of the sum of all distances to other nodes.Since your example is completely symmetric, we only calculate the closeness centrality of $A$.distance $A\to B$ is 1distance $A\to C$ is 1distance $A\to D$ is 2Therefore the sum of the distances is 4, and the closeness of $A$ is $1/4$. This shows that the NodeXL results are correct. I would advise you to have a look at the manual of Gephi to check how the closeness is computed here. It should be definitely be smaller than 1.