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Complex hypergraphs.

Alexei Vazquez1

  • 1Nodes & Links Ltd, Salisbury House, Station Road, Cambridge CB1 2LA, United Kingdom.

Physical Review. E
|March 18, 2023
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Summary
This summary is machine-generated.

Complex hypergraphs (chygraphs) offer a new way to represent complex systems, balancing detail with analytical insight. This study introduces chygraphs and demonstrates their use in analyzing system components and transitions.

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Area of Science:

  • Graph theory
  • Network science
  • Combinatorics

Background:

  • Representing complex systems with heterogeneous components is challenging.
  • Balancing analytical tractability with system heterogeneity is difficult.
  • Existing structures like hypergraphs and multilayer networks have limitations.

Purpose of the Study:

  • Introduce complex hypergraphs (chygraphs) as a unifying framework for complex systems.
  • Demonstrate the applicability of chygraphs through component size statistics and giant component transitions.
  • Develop a vectorization technique for analyzing the multilevel nature of chygraphs.

Main Methods:

  • Integration of concepts from hypergraphs, multilayer networks, simplicial complexes, and hyperstructures.
  • Calculation of component size statistics for complex hypergraphs.
  • Development and application of a novel vectorization technique for multilevel analysis.

Main Results:

  • Complex hypergraphs (chygraphs) provide a unified representation for diverse complex systems.
  • The vectorization technique effectively handles the multilevel nature of chygraphs.
  • Identification of the transition to a giant component within complex hypergraph structures.

Conclusions:

  • Chygraphs offer a powerful and unifying framework for modeling complex systems.
  • This structure allows for significant analytical insight into system properties.
  • Chygraphs bridge concepts from multiple mathematical fields for broader applicability.