Community detection by modularity maximization using GRASP with path relinking

Detection of community structure in graphs remains up to this date a computationally challenging problem despite the efforts of many researchers from various scientific fields in the past few years. The modularity value of a set of vertex clusters in a graph is a widely used quality measure for community structure, and the relating problem of finding a partition of the vertices into clusters such that the corresponding modularity is maximized is an NP-Hard problem. A Greedy Randomized Adaptive Search Procedure (GRASP) with path relinking is presented in this paper, for modularity maximization in undirected graphs. A new class of {0, 1} matrices is introduced which characterizes the family of clusterings in a graph, and a distance function is given which enables us to define an l-neighborhood local search which generalizes most of the related local search methods that have appeared in the literature. Computational experiments comparing the proposed algorithm with other heuristics from the literature in a set of some well known benchmark instances, indicate that our implementation of GRASP with path relinking consistently produces better quality solutions.