Identify the diversity of mesoscopic structures in networks: A mixed random walk approach

Community or cluster structure, which can provide insight into the natural partitions and inner connections of a network, is a key feature in studying the mesoscopic structure of complex systems. Although numerous methods for community detection have been proposed ever since, there is still a lack of understanding on how to quantify the diversity of pre-divided community structures, or rank the roles of communities in participating in specific dynamic processes. Inspired by the Law of Mass Action in chemical kinetics, we introduce here the community random walk energy (CRWE), which reflects a potential based on the diffusion phase of a mixed random walk process taking place on the network, to identify the configuration of community structures. The difference of CRWE allows us to distinguish the intrinsic topological diversity between individual communities, on condition that all the communities are pre-arranged in the network. We illustrate our method by performing numerical simulations on constructive community networks and a real social network with distinct community structures. As an application, we apply our method to characterize the diversity of human genome communities, which provides a possible use of our method in inferring the genetic similarity between human populations.