Identifying Relationship Patterns Inside Communities

Some studies on networks require to isolate groups of elements, known as Com-munities. Some examples include (i) detection of protein complexes [10]; (ii) mapping metabolic networks [9]; (iii) identification of criminal organizations [5]. There are many algorithms to find communities and a commonly used evalua-tion approach is the maximization of the Modularity Clustering. This technique was proposed by Newman and Girvan [7][11] and is based on the number of edges that are into a community minus the expected number of edges from null model. The null model is a graph G ′ = (V,E′), obtained from original network G = (V,E), with |E′ | = |E | and each edge is distributed over uniform prob-ability, so each node in G ′ has the same degree on equivalent node in G. The objective function is to maximize the Equation 12 u,v∈E( Au,v−(dudv) 2m)σ(u, v), where the dw is degree of w ∈ V, |E | = m and function σ returns 1, if u and