Community Division Metric Based on Persistent Homology

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