Reconstructing Mesoscale Network Structures

When facing the problem of reconstructing complex mesoscale network structures, it is generally believed that models encoding the nodes organization into modules must be employed. The present paper focuses on two block structures that characterize the empirical mesoscale organization of many real-world networks, i.e., the bow-tie and the core-periphery ones, with the aim of quantifying the minimal amount of topological information that needs to be enforced in order to reproduce the topological details of the former. Our analysis shows that constraining the network degree sequences is often enough to reproduce such structures, as confirmed by model selection criteria as AIC or BIC. As a byproduct, our paper enriches the toolbox for the analysis of bipartite networks, still far from being complete: both the bow-tie and the core-periphery structure, in fact, partition the networks into asymmetric blocks characterized by binary, directed connections, thus calling for the extension of a recently proposed method to randomize undirected , bipartite networks to the directed case.