Abstract
Detecting communities in a network, based only on the adjacency matrix, is a problem of interest to several scientific disciplines. Recently, Zhang and Moore have introduced an algorithm [Proc. Natl. Acad. Sci. USA 111, 18144 (2014)], called mod-bp, that avoids overfitting the data by optimizing a weighted average of modularity (a popular goodness-of-fit measure in community detection) and entropy (i.e., number of configurations with a given modularity). The adjustment of the relative weight, the “temperature” of the model, is crucial for getting a correct result from mod-bp. In this work we study the many phase transitions that mod-bp may undergo by changing the two parameters of the algorithm: the temperature and the maximum number of groups . We introduce a new set of order parameters that allow us to determine the actual number of groups , and we observe on both synthetic and real networks the existence of phases with any , which were unknown before. We discuss how to interpret the results of mod-bp and how to make the optimal choice for the problem of detecting significant communities.
1 More- Received 16 June 2015
- Revised 22 September 2015
DOI:https://doi.org/10.1103/PhysRevE.92.042804
©2015 American Physical Society