Analysis of the structure of complex networks at different resolution levels

Abstract

Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights into the structure- functionality relationship. The standard approach is based on the optimization of a quality function, modularity, which is a relative quality measure for the partition of a network into modules. Recently, some authors (Fortunato and Barthélemy 2007 Proc. Natl Acad. Sci. USA 104 36 and Kumpula et al 2007 Eur. Phys. J. B 56 41) have pointed out that the optimization of modularity has a fundamental drawback: the existence of a resolution limit beyond which no modular structure can be detected even though these modules might have their own entity. The reason is that several topological descriptions of the network coexist at different scales, which is, in general, a fingerprint of complex systems. Here, we propose a method that allows for multiple resolution screening of the modular structure. The method has been validated using synthetic networks, discovering the predefined structures at all scales. Its application to two real social networks allows us to find the exact splits reported in the literature, as well as the substructure beyond the actual split. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.