2011/07/31 by Andrea Lancichinetti, Santo Fortunato · 504 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Benchmark (surveying) #Bioinformatics and Genomic Networks #Community structure #Complex Network Analysis Techniques #Computer science #Limit (mathematics) #Mathematical optimization #Mathematics #Maximization #Merge (version control) #Modularity (biology) #Opinion Dynamics and Social Influence #Resolution (logic) #Statistics #cs.SI #physics.soc-ph
paper · pdf · doi:10.1103/physreve.84.066122
published in Physical Review E 84(6), 066122 (American Physical Society) · 9 pages, 9 figures. Analysis extended to other global optimization methods. Final version published in Physical Review E
openalex publication_date 2011/12/27 · arxiv created 2012/02/12 · arxiv updated 2012/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Modularity maximization is the most popular technique for the detection of community structure in graphs. The resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure, with tunable resolution parameters. We show that multiresolution modularity suffers from two opposite coexisting problems: the tendency to merge small subgraphs, which dominates when the resolution is low; the tendency to split large subgraphs, which dominates when the resolution is high. In benchmark networks with heterogeneous distributions of cluster sizes, the simultaneous elimination of both biases is not possible and multiresolution modularity is not capable to recover the planted community structure, not even when it is pronounced and easily detectable by other methods, for any value of the resolution parameter. This holds for other multiresolution techniques and it is likely to be a general problem of methods based on global optimization.