Deciphering Network Community Structure by Surprise

TL;DR

This paper introduces a new global parameter called Surprise (S) for characterizing community structures in complex networks, demonstrating its superior performance over traditional methods like modularity in synthetic and real networks.

Contribution

The paper proposes and validates Surprise (S) as a novel, effective global criterion for community detection, outperforming existing methods like modularity.

Findings

S effectively characterizes community structure in synthetic networks.

S outperforms modularity in benchmark tests.

Application to real networks yields meaningful partitions.

Abstract

The analysis of complex networks permeates all sciences, from biology to sociology. A fundamental, unsolved problem is how to characterize the community structure of a network. Here, using both standard and novel benchmarks, we show that maximization of a simple global parameter, which we call Surprise (S), leads to a very efficient characterization of the community structure of complex synthetic networks. Particularly, S qualitatively outperforms the most commonly used criterion to define communities, Newman and Girvan's modularity (Q). Applying S maximization to real networks often provides natural, well-supported partitions, but also sometimes counterintuitive solutions that expose the limitations of our previous knowledge. These results indicate that it is possible to define an effective global criterion for community structure and open new routes for the understanding of complex networks.