Detecting core-periphery structures by surprise

Detecting the presence of mesoscale structures in complex networks is of primary importance. This is especially true for financial networks, whose structural organization deeply affects their resilience to events like default cascades, shocks propagation, etc. Several methods have been proposed, so far, to detect communities, i.e., groups of nodes whose internal connectivity is significantly large. Communities, however do not represent the only kind of mesoscale structures characterizing real-world networks: other examples are provided by bow-tie structures, core-periphery structures and bipartite structures. Here we propose a novel method to detect statistically significant bimodular structures, i.e., either bipartite or core-periphery ones. It is based on a modification of the surprise, recently proposed for detecting communities. Our variant allows for bimodular nodes partitions to be revealed, by letting links to be placed either 1) within the core part and between the core and the periphery parts or 2) between the layers of a bipartite network. From a technical point of view, this is achieved by employing a multinomial hypergeometric distribution instead of the traditional, binomial hypergeometric one; as in the latter case, this allows a p-value to be assigned to any given (bi)partition of the nodes. To illustrate the performance of our method, we report the results of its application to several real-world networks, including social, economic and financial ones.