Closed walks for community detection

• Our method performs well on computer generated networks and real-world networks.
• Closed walks of small orders are basic elements in constructing community structure.
• Our method is a better tradeoff of accuracy and runtime.
• Our method is a novel way to solve the double peak structure problem.
• Our work can provide us with a new perspective for understanding community structure in complex networks.

In this paper, we propose a novel measure that integrates both the concept of closed walks and clustering coefficients to replace the edge betweenness in the well-known divisive hierarchical clustering algorithm, the Girvan and Newman method (GN). The edges with the lowest value are removed iteratively until the network is degenerated into isolated nodes. The experimental results on computer generated networks and real-world networks showed that our method makes a better tradeoff of accuracy and runtime. Based on the analysis of the results, we observe that the nontrivial closed walks of order three and four can be considered as the basic elements in constructing community structures. Meanwhile, we discover that those nontrivial closed walks outperform trivial closed walks in the task of analyzing the structure of networks. The double peak structure problem is mentioned in the last part of the article. We find that our proposed method is a novel way to solve the double peak structure problem. Our work can provide us with a new perspective for understanding community structure in complex networks.