Limitation of multi-resolution methods in community detection

TL;DR

This paper reveals fundamental limitations of multi-resolution community detection methods, showing they may prematurely split large communities and depend on community interconnectedness and size differences, not network size.

Contribution

It provides a theoretical analysis of the intrinsic limitations of multi-resolution modularity methods in community detection.

Findings

Large communities may split before small ones become visible.

Limitations depend on community interconnectedness and size differences.

Findings confirmed in various example networks.

Abstract

Recently, a type of multi-resolution methods in community detection was introduced, which can adjust the resolution of modularity by modifying the modularity function with tunable resolution parameters, such as those proposed by Arenas, Fernandez and Gomez and by Reichardt and Bornholdt. In this paper, we show that these methods still have the intrinsic limitation-large communities may have been split before small communities become visible-because it is at the cost of the community stability that the enhancement of the modularity resolution is obtained. The theoretical results indicated that the limitation depends on the degree of interconnectedness of small communities and the difference between the sizes of small communities and of large communities, while independent of the size of the whole network. These findings have been confirmed in several example networks, where communities even are full-completed sub-graphs.