Surprise maximization reveals the community structure of complex networks

TL;DR

This paper introduces Surprise, a new quality function for community detection in complex networks, demonstrating that maximizing Surprise yields more accurate community structures than traditional methods based on modularity.

Contribution

The study proposes Surprise as a novel measure for community detection and shows that maximizing it outperforms existing algorithms based on modularity.

Findings

Surprise effectively identifies true community structures.

Maximizing Surprise outperforms modularity-based methods.

Combining multiple algorithms and selecting the highest Surprise solution improves accuracy.

Abstract

How to determine the community structure of complex networks is an open question. It is critical to establish the best strategies for community detection in networks of unknown structure. Here, using standard synthetic benchmarks, we show that none of the algorithms hitherto developed for community structure characterization perform optimally. Significantly, evaluating the results according to their modularity, the most popular measure of the quality of a partition, systematically provides mistaken solutions. However, a novel quality function, called Surprise, can be used to elucidate which is the optimal division into communities. Consequently, we show that the best strategy to find the community structure of all the networks examined involves choosing among the solutions provided by multiple algorithms the one with the highest Surprise value. We conclude that Surprise maximization precisely reveals the community structure of complex networks.