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The present paper focuses on two block structures that characterize the empirical mesoscale organization of many real\u2010world networks, i.e., the <jats:italic>bow-tie<\/jats:italic> and the <jats:italic>core-periphery<\/jats:italic> 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\u2010tie and the core\u2010periphery 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 <jats:italic>undirected<\/jats:italic>, bipartite networks to the <jats:italic>directed<\/jats:italic> case.<\/jats:p>","DOI":"10.1155\/2019\/5120581","type":"journal-article","created":{"date-parts":[[2019,1,10]],"date-time":"2019-01-10T23:32:17Z","timestamp":1547163137000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Reconstructing Mesoscale Network Structures"],"prefix":"10.1155","volume":"2019","author":[{"given":"Jeroen","family":"van Lidth de Jeude","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8005-6351","authenticated-orcid":false,"given":"Riccardo","family":"Di Clemente","sequence":"additional","affiliation":[]},{"given":"Guido","family":"Caldarelli","sequence":"additional","affiliation":[]},{"given":"Fabio","family":"Saracco","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9011-966X","authenticated-orcid":false,"given":"Tiziano","family":"Squartini","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,1,10]]},"reference":[{"key":"e_1_2_12_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2009.11.002"},{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.09.002"},{"key":"e_1_2_12_3_2","unstructured":"KhanB. 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