Detecting mesoscale structures by surprise

The importance of identifying mesoscale structures in complex networks can be hardly overestimated. So far, much attention has been devoted to detect modular and bimodular structures on binary networks. This effort has led to the definition of a framework based upon the score function called ‘surprise’, i.e. a p-value that can be assigned to any given partition of nodes. Hereby, we make a step further and extend the entire framework to the weighted case: six variants of surprise, induced by just as many variants of the hypergeometric distribution, are, thus, considered. As a result, a general, statistically grounded approach for detecting mesoscale network structures via a unified, suprise-based framework is presented. To illustrate its performances, both synthetic benchmarks and real-world configurations are considered. Moreover, we attach to the paper a Python code implementing all variants of surprise discussed in the present manuscript.