Community Division Metric Based on Persistent Homology

Abstract

Community structure is one of the most important structural features of complex networks. However, most of the existing community division metrics only consider the relationship between nodes, and do not consider the overall closeness of the internal and external communities from the perspective of topology. Persistent homology (PH) is a mathematical tool in computational topology, which can capture high-dimensional topological features and is widely used in the analysis of complex networks. In this paper, we define a community partitioning metric based on persistent homology theory, and propose an algorithm of community division based on CPH which provides a new method for community partitioning performance. From the validation experiments, the Louvain algorithm is used to evaluate the community partitioning performance of social networks, and the experimental results show that community division metric based on persistent homology can measure the performance of community partitioning from the perspective of topology, persistent homology can be used as a new way to describe community structure.