> Is the algorithm of community detection in weighted (directed or
> undirected) graphs introduced in:
> 
> Community structure in directed networks, E. A. Leicht and M. E. J.
> Newman, Phys. Rev. Lett. 100, 118703 (2008).
> 
> has been implemented through igraph?
As far as I know, this algorithm is essentially Newman's leading eigenvector 
method; for directed graphs, there is a modification in the modularity function 
which accounts for the different in- and out-degrees of the vertices. The 
undirected version is implemented in igraph as the "leading eigenvector method".

Best,
Tamas


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