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Hi-C: A Method to Study the Three-dimensional Architecture of Genomes.
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The microscale organization of directed hypergraphs.

Quintino Francesco Lotito1,2, Alberto Vendramini2, Alberto Montresor2

  • 1Department of Network and Data Science, Central European University, Vienna, Austria.

Communications Physics
|February 20, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a framework to analyze directed hypergraphs, revealing the microscale structure of higher-order interactions in complex systems. It quantifies connectivity patterns and identifies recurring interaction motifs in real-world data.

Keywords:
Complex networksComputational science

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Area of Science:

  • Network Science
  • Complex Systems Analysis
  • Graph Theory

Background:

  • Real-world systems often involve complex interactions beyond simple pairwise links.
  • Undirected hypergraphs model higher-order interactions but lack directionality.
  • Directed hypergraphs capture directional information flow in complex networks.

Purpose of the Study:

  • To develop a framework for characterizing the microscale structural organization of directed hypergraphs.
  • To analyze higher-order connectivity patterns and identify recurring interaction motifs.
  • To provide tools for quantifying directionality and reciprocity in complex systems.

Main Methods:

  • Extraction of directed hypergraph 'fingerprints' based on hyperedge source and target sizes.
  • Analysis of overlap among sources and targets to identify co-sending and co-receiving nodes.
  • Definition and quantification of exact, strong, and weak reciprocity in hypergraphs.
  • Extension of motif analysis to identify recurring interaction patterns.

Main Results:

  • The framework successfully characterizes microscale structures in directed hypergraphs.
  • Analysis revealed distinct higher-order connectivity patterns across various real-world systems.
  • The study identified recurring sets of co-sending and co-receiving nodes.
  • Reciprocity measures and motif analysis provided insights into network organization.

Conclusions:

  • The developed framework offers a comprehensive approach to understanding directed higher-order networks.
  • It reveals fundamental structural principles governing real-world systems like Bitcoin transactions and metabolic networks.
  • This work advances the analysis of complex systems with directional higher-order interactions.