Enhance the efficiency of heuristic algorithms for maximizing the modularity Q

The Modularity Q is an important index for identifying the community structure in complex networks. Maximizing Q has been proved to be an NP problem and it can only be achieved by heuristic algorithms. In this paper, the modularity maximization problem is proved to be a nonconvex quadratic programming problem. Based on this result, an approach is suggested and tested to improve the efficiency of heuristic algorithms for maximizing the modularity Q. Many numerical results demonstrate that the approach is effective.