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The analysis of complex networks permeates all sciences, from biology tosociology. A fundamental, unsolved problem is how to characterize the communitystructure of a network. Here, using both standard and novel benchmarks, we showthat maximization of a simple global parameter, which we call Surprise (S),leads to a very efficient characterization of the community structure ofcomplex synthetic networks. Particularly, S qualitatively outperforms the mostcommonly 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 thatexpose the limitations of our previous knowledge. These results indicate thatit is possible to define an effective global criterion for community structureand open new routes for the understanding of complex networks.

Deciphering Network Community Structure by Surprise