An algorithm for network community structure determination by surprise

Abstract

A community in a network is an intuitive idea for which there is no consensus on its objective mathematical definition. Therefore, different algorithms and metrics have been suggested in order to identify these structures in graphs. In this work, we propose a new benchmark and a new approach based on a metric known as surprise. We compare our approach to several others in the literature, in different kinds of benchmarks, including our own (that tackles separately the different ways in which one may degrade a network’s community structure) and discuss the different biases we identify for each algorithm and benchmark. In particular, we identify a possible flaw in the way the LFR benchmark constructs its communities and that algorithms suffering from bad resolution are biased towards identifying communities with similar sizes. We show that the surprise based approaches perform better than the modularity based ones, specially for heterogeneous graphs (with very different community sizes coexisting).