{"authors":[{"id":"orcid_______::1278d8fab9f7668e923f25a3740b7529","fullName":"Quintino Francesco Lotito","name":"Quintino Francesco","surname":"Lotito","rank":1,"pid":{"id":{"scheme":"orcid","value":"0000-0001-7084-8339"},"provenance":null}},{"id":null,"fullName":"Alberto Vendramini","name":"Alberto","surname":"Vendramini","rank":2,"pid":null},{"id":null,"fullName":"Alberto Montresor","name":"Alberto","surname":"Montresor","rank":3,"pid":null},{"id":null,"fullName":"Federico Battiston","name":"Federico","surname":"Battiston","rank":4,"pid":{"id":{"scheme":"orcid_pending","value":"0000-0001-9646-6232"},"provenance":null}}],"openAccessColor":"gold","publiclyFunded":false,"eoscIfGuidelines":null,"type":"publication","language":{"code":"eng","label":"English"},"countries":[{"code":"AT","label":"Austria","provenance":null}],"subjects":[{"subject":{"scheme":"keyword","value":"Social and Information Networks (cs.SI)"},"provenance":null},{"subject":{"scheme":"keyword","value":"FOS: Computer and information sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"FOS: Physical sciences"},"provenance":null},{"subject":{"scheme":"FOS","value":"0102 computer and information sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"Physics and Society (physics.soc-ph)"},"provenance":null},{"subject":{"scheme":"keyword","value":"Physics and Society"},"provenance":null},{"subject":{"scheme":"keyword","value":"Social and Information Networks"},"provenance":null},{"subject":{"scheme":"FOS","value":"01 natural sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"Article"},"provenance":null}],"mainTitle":"The microscale organization of directed hypergraphs","subTitle":null,"descriptions":["Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within each hyperedge, and allow to account for the directional flow of information between nodes. Here, we provide a framework to characterize the structural organization of directed higher-order networks at their microscale. First, we extract the fingerprint of a directed hypergraph, capturing the frequency of hyperedges with a certain source and target sizes, and use this information to compute differences in higher-order connectivity patterns among real-world systems. Then, we formulate reciprocity in hypergraphs, including exact, strong, and weak definitions, to measure to which extent hyperedges are reciprocated. Finally, we extend motif analysis to identify recurring interaction patterns and extract the building blocks of directed hypergraphs. We validate our framework on empirical datasets, including Bitcoin transactions, metabolic networks, and citation data, revealing structural principles behind the organization of real-world systems.","In press in Communications Physics"],"publicationDate":"2026-01-07","publisher":"Springer Science and Business Media LLC","embargoEndDate":"2024-10-01","sources":["Crossref","Commun Phys"],"formats":null,"contributors":null,"coverages":null,"bestAccessRight":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/"},"container":{"name":"Communications 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