  Identifying community structure in networks is an issue of particular
interest in network science. The modularity introduced by Newman and Girvan
[Phys. Rev. E 69, 026113 (2004)] is the most popular quality function for
community detection in networks. In this study, we identify a problem in the
concept of modularity and suggest a solution to overcome this problem.
Specifically, we obtain a new quality function for community detection. We
refer to the function as Z-modularity because it measures the Z-score of a
given division with respect to the fraction of the number of edges within
communities. Our theoretical analysis shows that Z-modularity mitigates the
resolution limit of the original modularity in certain cases. Computational
experiments using both artificial networks and well-known real-world networks
demonstrate the validity and reliability of the proposed quality function.
