Inverse order of Closeness and Normalized one? Why?

[Jeremyhl]

Hi,

I had a weighted and directed network, and I found Gephi made an interesting result that orders of nodes whose ordering criteria were Closeness and Normalized Closeness were different, and even exactly inverse. It would be easier to understand the current situation if you see a picture below:

I have known that the order of nodes is no difference no matter what index I use either centrality or normalized centrality. Why are those orders different, even exactly inverse?
Thanks.

------------- In addition,---------------

I found that inverse relationship is exactly reciprocal.
Thus, this is my key question.
Why does Gephi produce normalized closeness by using a simple reciprocal number of closeness centrality?

[chiinook]

I am no mathematician, but according to what I have read what is being reported in Gephi as closeness might be better understood as "farness".

Farness actually makes logical sense when we talk about distance, much more so than "closeness". Graph Closeness is a measure of the average distance from a node to every other node in the network. But in order to move from a measure of "how FAR away" to "how CLOSE away", that average is typically inverted (normalized) so that the results fit between 0 and 1.

The standard closeness algorhythm in Gephi doesn't normalize closeness by default. So higher numbers are indicating distance ("farness") rather than rank ("closeness"). Gephi gives us the inverse of what we are looking for, which is why changing node size by Closeness Ranking produces the opposite of what you might expect.

You can pump the same data into NodeXL for example and get normalized closeness by default.

I would imagine there is a reason that Gephi decided to do things this way, but I'm not sure what the advantage would be. I am also not certain how to rank according to the inverse. That would be very handy to know!

Open to corrections and wisdom from more informed members!

Matt Edminster