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How to determine the community structure of complex networks is an openquestion. It is critical to establish the best strategies for communitydetection in networks of unknown structure. Here, using standard syntheticbenchmarks, we show that none of the algorithms hitherto developed forcommunity structure characterization perform optimally. Significantly,evaluating the results according to their modularity, the most popular measureof the quality of a partition, systematically provides mistaken solutions.However, a novel quality function, called Surprise, can be used to elucidatewhich is the optimal division into communities. Consequently, we show that thebest strategy to find the community structure of all the networks examinedinvolves choosing among the solutions provided by multiple algorithms the onewith the highest Surprise value. We conclude that Surprise maximizationprecisely reveals the community structure of complex networks.

Surprise maximization reveals the community structure of complex networks