The Influence of NMI against Modularity in Community Detection Problem: A Case Study for Unsigned and Signed Networks

Abstract

Community detection is useful for better understanding the structure of complex networks. It aids in the extraction of the required information from such networks and has a vital role in different fields that range from healthcare to regional geography, economics, human interactions, and mobility. The method for detecting the structure of communities involves the partitioning of complex networks into groups of nodes, with extensive connections within community and sparse connections with other communities. In the literature, two main measures, namely the Modularity (Q) and Normalized Mutual Information (NMI) have been used for evaluating the validation and quality of the detected community structures. Although many optimization algorithms have been implemented to unfold the structures of communities, the influence of NMI on the Q, and vice versa, between a detected partition and the correct partition in signed and unsigned networks is unclear. For this reason, in this paper, we investigate the correlation between Q and NMI in signed and unsigned networks. The results show that there is no direct relationship between Q and NMI in both types of networks.