Narrow scope for resolution-limit-free community detection

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-07, Vol.84 (1 Pt 2), p.016114-016114, Article 016114
• Main Authors: Traag, V A, Van Dooren, P, Nesterov, Y
• Format: Article
• Language: English
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/physreve.84.016114

Detecting communities in large networks has drawn much attention over the years. While modularity remains one of the more popular methods of community detection, the so-called resolution limit remains a significant drawback. To overcome this issue, it was recently suggested that instead of comparing the network to a random null model, as is done in modularity, it should be compared to a constant factor. However, it is unclear what is meant exactly by "resolution-limit-free," that is, not suffering from the resolution limit. Furthermore, the question remains what other methods could be classified as resolution-limit-free. In this paper we suggest a rigorous definition and derive some basic properties of resolution-limit-free methods. More importantly, we are able to prove exactly which class of community detection methods are resolution-limit-free. Furthermore, we analyze which methods are not resolution-limit-free, suggesting there is only a limited scope for resolution-limit-free community detection methods. Finally, we provide such a natural formulation, and show it performs superbly.