Re: [igraph] RE: A measure of closeness

[Tamas Nepusz]

Dear David,

> I have a large undirected graph for which the nodes fall into a number
> of classes. I would like to know whether the nodes in each class tend
> to clump - to be close to each other. What would be a good measure of
> 'closeness'? If it could be calculated efficiently then I could
> compare the observed value with values obtained by permuting the class
> assignments.
I'd try the modularity measure first. Modularity quantifies the
difference between the actual number of edges going between nodes of the
same class and the expected number of such edges if the network was
completely random with the same degree distribution. Positive modularity
signifies that you have more edges within nodes of the same class than
what you would expect from a randomized network. Modularity is
implemented in igraph_modularity() if you are using C, modularity() if
you are using R. If you are using Python, there is a modularity() method
of the Graph object.

-- 
Tamas