The Maximum Community Partition Problem in Networks

We proposed a community structure detection problem which aims to analyze the relationships among the data via the network topology. We collect a series of unified definitions for community structures and formulate the community structure detection into a combinatorial optimization problem to identify as many communities as possible for a given network. For some well known community definitions, we prove that there is no polynomial time optimal solution for this maximum partition problem unless P = NP, and we develop a heuristic algorithm based on greedy strategy for it. The experimental results on many real networks show that the proposed algorithm is effective in terms of the number of valid communities and the modularity score.