Detecting mesoscale structures by surprise

The importance of identifying the presence mesoscale structures in complex networks can be hardly overestimated. So far, much attention has been devoted to detection communities, bipartite and core-periphery on binary networks: such an effort led definition a unified framework based upon score function called surprise, i.e. p-value that assigned any given partition nodes, both undirected directed networks. Here, we aim at making step further, by extending entire weighted case: after reviewing application surprise-based formalism structures, present suitable generalization it for detecting topic received less attention. To this aim, analyze four variants surprise; from technical point view, amounts employing hypergeometric distribution: binomial one multinomial "bimodular" their negative counterparts communities On top that, define two "enhanced" able encode constraints whose rests generalizations distribution itself. As result, general, statistically-grounded approach detect via unified, suprise-based framework. illustrate performance our methods, we, first, test them variety well-established, synthetic benchmarks and, then, apply several real-world networks, social, economic, financial ecological ones. Moreover, attach paper Python code implementing all considered surprise.