A cutting plane algorithm for Modularity maximization with heuristics for separation problem

Abstract

The modularity proposed by Newman and Girvan is the most commonly used measure when the nodes of a graph are grouped into communities consisting of tightly connectednodes. We formulate the modularity maximization problem as a set partitioning problem, and propose an algorithm for the problem based on the linear programming relaxation. We solve the dual of the linear programming relaxation by using a cutting plane method. To mediate the slow convergence that cutting plane methods usually suffer, we propose a method for finding and simultaneously adding multiple cutting planes which may complement well each other