I'm using CommunityStructureAssginment from GraphUtilities but not sure what is the algorithm behind it.
May be someone knows what is the algorithm? Or any info on the community structure identification algorithms implemented in Mathematica?
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The GraphUtilities documentation has a whole section that should answer your question: “Algorithms for Finding Community Structure”. The reference for the algorithm it uses is: A. Clauset, "Finding Local Community Structure in Networks," Physical Review E, 72, 026132, 2005 (arXiv mirror).