On the Lower Bound of Modularity for Graph Fission

Abstract

Among the tools available for analysis of manifold data in modern signal processing is the popular modularity method. Hugely successful, modularity is not without its degeneracies, specifically with regard to its ability to observe smaller community structure in larger contexts. A body of work has been built around this so-called resolution limit of modularity. However, the current analytical bounds do not describe the resolution limit in the context of single-cut graph fission. In this paper, we present a new resolution limit to this end and show its effect on both synthetic and real-world networks.