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Measuring dynamical systems on directed hypergraphs.

Mauro Faccin1

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Summary
This summary is machine-generated.

This study introduces a method to analyze complex systems using higher-order graphs by examining their associated dynamical systems. This approach simplifies the measurement of network properties in hypergraphs, avoiding computational complexity.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Graph theory

Background:

  • Traditional network models use pairwise interactions, failing to capture higher-order systems.
  • Higher-order graphs offer better modeling but increase computational complexity.

Purpose of the Study:

  • To analyze the interplay between directed hypergraph structures and linear dynamical systems (random walks).
  • To extend network measures like centrality and modularity to higher-order graph frameworks.
  • To propose a method that avoids the computational complexity of redefining measures for hypergraphs.

Main Methods:

  • Defining a random walk on a directed hypergraph.
  • Analyzing the dynamical system associated with the hypergraph structure.
  • Applying existing network measures to pairwise structures within the dynamical system, such as the transition matrix.

Main Results:

  • The study proposes measuring the dynamical system associated with a hypergraph instead of redefining network measures.
  • This approach allows the application of known measures to pairwise structures.
  • A family of measures amenable to this procedure is identified.

Conclusions:

  • Analyzing the dynamical system of a hypergraph offers a computationally efficient way to extend network analysis.
  • This method provides a practical approach to understanding complex systems with higher-order interactions.