A Constrained Louvain Algorithm with a Novel Modularity

Community detection is a significant and challenging task in network research. Nowadays, many community detection methods have been developed. Among them, the classical Louvain algorithm is an excellent method aiming at optimizing an objective function. In this paper, we propose a modularity function F2 as a new objective function. Our modularity function F2 overcomes certain disadvantages of the modularity functions raised in previous literature, such as the resolution limit problem. It is desired as a competitive objective function. Then, the constrained Louvain algorithm is proposed by adding some constraints to the classical Louvain algorithm. Finally, through the comparison, we have found that the constrained Louvain algorithm with F2 is better than the constrained Louvain algorithm with other objective functions on most considered networks. Moreover, the constrained Louvain algorithm with F2 is superior to the classical Louvain algorithm and the Newman’s fast method.