Re: [igraph] Calculating Q-Spa modularity for spatially embedded networks

[Tamas Nepusz]

> I am no mathematician, but can code OK in R. From the look of equations, I 
> am guessing that practically it will mean creating another matrix 
> containing the pairwise distances between nodes, then.. well that's when it 
> gets fuzzy.
In a first (rough and not scalable) implementation, you will need three
matrices (let's neglect the weights for now):

A - the adjacency matrix of the graph where A_{ij} is 1 if i and j are
connected, zero otherwise.

P - the null model matrix which you obtain from Eqs (5) and (6)

delta - a matrix where delta_{ij} is 1 if i and j are in the same cluster,
zero otherwise.

The modularity is then simply the sum of the elements in the *elementwise*
product of (A-P) and delta, divided by 2m (which is the sum of elements in
A). I don't know how to implement this in R, but I hope this helps anyway.

If you implement this, an easy way to check your implementation is to take
an undirected graph and make P equal to d * d', where d is the column vector
of vertex degrees. Your function should then give the same results as
igraph's built-in modularity() function.

-- 
Tamas