Some properties of e-quality function for network clustering

One of the most important properties of graphs that represents real complex systems is community structure, or clustering, i.e., organizing 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 analyze Exponential Quality function for network clustering. We consider different classes of artificial networks from literature and analyze 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 show that Exponential Quality function detects the expected and reasonable clusters in all classes of instances and the Modularity function does not.