Modularity Maximization in Complex Networks

Years and Authors of Summarized Original Work

• 2013; Dinh, Thai

• 2013; Dinh, Nguyen, Alim, Thai

• 2013; DasGupta, Desai

• 2014; Dinh, Thai

Problem Definition

Many complex networks of interests such as the Internet, social, and biological networks exhibit the community structure where nodes are naturally clustered into tightly connected communities, with only sparser connections between them. The modularity maximization is concerned with finding such community structures in a given complex network.

Consider a network represented as an undirected graph G = (V, E) consisting of n =  | V | vertices and m =  | E | edges. The adjacency matrix of G is denoted by $\boldsymbol{A} = \left (A_{ij}\right )$, where A _ij is the weight of edge (i, j) and A _ij  = 0 if (i, j) ∉ E. We also denote the (weighted) degree of vertex i, the total weights of edges incident at i, by deg(i) or, in short, d _i .

Community structure (CS) is a division of the vertices in Vinto a collection of disjoint subsets of...