Research Article Reconstructing Mesoscale Network Structures Jeroen van Lidth de Jeude, 1 Riccardo Di Clemente , 2 Guido Caldarelli, 1 Fabio Saracco, 1 and Tiziano Squartini 1 1 IMT School for Advanced Studies, Piazza S. Francesco 19, 55100 Lucca, Italy 2 University College London, Te Bartlett Centre for Advanced Spatial Analysis, Gower Street, WC1E 6BT London, UK Correspondence should be addressed to Tiziano Squartini; tiziano.squartini@imtlucca.it Received 19 February 2018; Revised 5 December 2018; Accepted 19 December 2018; Published 10 January 2019 Academic Editor: Lucas Lacasa Copyright © 2019 Jeroen van Lidth de Jeude et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. Te 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 ofen enough to reproduce such structures, as confrmed 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. 1. Introduction Te analysis of mesoscale network structures is a topic of great interest within the community of network scien- tists: much attention, however, has been received by the community-detection topic [1–3], while the analysis of other mesostructures has remained far less explored. Te present work aims at contributing to this stream of research, by exploring the efectiveness of models that constrain only local information in reproducing complex mesostructures as the bow-tie and the core-periphery ones. When approaching such a problem it is, in fact, commonly believed that models encoding the nodes organization into modules must be employed: here we test this hypothesis, by comparing models that enforce topological information like the total number of links, the degree sequences, and the reciprocity structure with their block-wise counterparts. To this aim, we have considered real-world networks whose topological structure is empirically characterized by bow-tie and core-periphery structures: both are character- ized by a central, cohesive subgraph surrounded by a loosely connected set of nodes [4]; in the frst case, however, the central part of the network has a fan-in and a fan-out- component, respectively, entering into and exiting from it. Remarkably, all models considered in the present paper can be recovered within the same framework, i.e., the entropy-maximization one, which has been proven to be rather efective for approaching both pattern detection and real-world networks reconstruction problems [5, 6]. Such a framework allows a tunable likelihood function to be defnable for each considered model, thus allowing selection criteria like AIC or BIC to be applicable for unambiguously determining the “winner” between competing models, i.e., the one carrying the right amount of information to account for the inspected structures. As a byproduct, our paper enriches the toolbox for the analysis of bipartite networks. Among the many, avail- able, network representations, the bipartite one has recently received much attention [7, 8]. Tis, in turn, has led to the def- inition of algorithms for randomizing [9–12], reconstructing [13] or projecting [14, 15] undirected, bipartite networks. Teir directed representation, however, has not been explored yet, thus calling for the defnition of techniques to approach the study of this kind of networks as well. Hindawi Complexity Volume 2019, Article ID 5120581, 13 pages https://doi.org/10.1155/2019/5120581