Hierarchical multiresolution method to overcome the resolution limit in complex networks

Abstract: The analysis of the modular structure of networks is a major challenge in complex networks theory. The validity of the modular structure obtained is essential to confront the problem of the topology-functionality relationship. Recently, several authors have worked on the limit of resolution that different community detection algorithms have, making impossible the detection of natural modules when very different topological scales coexist in the network. Existing multiresolution methods are not the panacea for solving the problem in extreme situations, and also fail. Here, we present a new hierarchical multiresolution scheme that works even when the network decomposition is very close to the resolution limit. The idea is to split the multiresolution method for optimal subgraphs of the network, focusing the analysis on each part independently. We also propose a new algorithm to speed up the computational cost of screening the mesoscale looking for the resolution parameter that best splits every subgraph. The hierarchical algorithm is able to solve a difficult benchmark proposed in [Lancichinetti & Fortunato, 2011], encouraging the further analysis of hierarchical methods based on the modularity quality function.