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The microscale organization of directed hypergraphs
Lotito, Quintino Francesco Vendramini, Alberto Montresor, Alberto Battiston, Federico
Lotito, Quintino Francesco
Vendramini, Alberto
Montresor, Alberto
Battiston, Federico
Title / Series / Name
Communications Physics
Publication Volume
9
Publication Issue
1
Pages
Editors
Keywords
General Physics and Astronomy
Files
URI
https://hdl.handle.net/20.500.14018/28824
Abstract
Many real-world systems exhibit higher-order interactions beyond pairwise links. Such interactions are modeled by undirected hypergraphs where edges can connect any number of vertices, but without capturing the directional nature of many real-world interactions. Directed hypergraphs overcome this limitation by distinguishing source and target sets within each hyperedge, enabling analysis of directional information flow. Here, we provide a framework to characterize the structural organization of directed higher-order networks at their microscale. 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 investigate the overlap among sources and targets to reveal recurring sets of co-sending and co-receiving nodes. We define reciprocity in hypergraphs using exact, strong, and weak definitions to quantify the extent to which 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.
Topic
Publisher
Place of Publication
Type
Journal article
Date
2026-01
Language
ISBN
Identifiers
10.1038/s42005-025-02472-9