  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.
