Multi-resolution community detection based on generalized self-loop rescaling strategy

• A generalized self-loop rescaling strategy for community detection is designed.
• One uniform ansatz for multi-resolution community detection methods is proposed.
• The performance of the derived methods in test networks is validated.
• The application of the existing modularity optimization algorithms is extended.
• The relationship between the methods and other methods is discussed.

Community detection is of considerable importance for analyzing the structure and function of complex networks. Many real-world networks may possess community structures at multiple scales, and recently, various multi-resolution methods were proposed to identify the community structures at different scales. In this paper, we present a type of multi-resolution methods by using the generalized self-loop rescaling strategy. The self-loop rescaling strategy provides one uniform ansatz for the design of multi-resolution community detection methods. Many quality functions for community detection can be unified in the framework of the self-loop rescaling. The resulting multi-resolution quality functions can be optimized directly using the existing modularity-optimization algorithms. Several derived multi-resolution methods are applied to the analysis of community structures in several synthetic and real-world networks. The results show that these methods can find the pre-defined substructures in synthetic networks and real splits observed in real-world networks. Finally, we give a discussion on the methods themselves and their relationship. We hope that the study in the paper can be helpful for the understanding of the multi-resolution methods and provide useful insight into designing new community detection methods.