Some Properties of E-quality Function for Network Clustering

Abstract

One of the most important properties of graphs that represents real complex systems is community structure, or clustering, i. e. ,organization vertices in cohesive groups with high concentration of edges within individual groups and low concentration of edges between vertices in different groups. In this paper, we analyzed Exponential Quality function for network clustering. We considered different classes of artificial network from the literature, and analyzed whether the maximization of Exponential Quality function tends
to merge or split clusters in optimal partition even if they are  unambiguously defined.
Our theoretical results showed that Exponential Quality function detects the expected and reasonable clusters in all classes of instances but the modularity function does not.