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Structural Reducibility of Hypergraphs
Alec Kirkley1,2,3, Helcio Felippe4, Federico Battiston4
1University of Hong Kong, Institute of Data Science, Hong Kong SAR, China.
Physical Review Letters
|January 2, 2026
Summary
This study introduces an information-theoretic framework to simplify complex system analysis. It identifies and removes redundant higher-order interactions in networks, preserving essential structures for clearer understanding.
Area of Science:
- Network science
- Information theory
- Complex systems analysis
Background:
- Traditional pairwise interactions offer limited insight into complex systems.
- Higher-order network analysis provides deeper understanding but faces interpretation and computational challenges.
Purpose of the Study:
- To develop a framework for assessing structural redundancy in hypergraph representations of complex systems.
- To identify critical higher-order interactions for simplifying network analysis.
- To enable the removal of redundancies while preserving essential network structures.
Main Methods:
- Utilizing an information-theoretic framework.
- Analyzing hypergraph representations of networked systems.
- Quantifying structural redundancy and identifying critical interaction orders.
Main Results:
- A method to determine the extent of structural redundancy in higher-order network representations.
- Identification of key higher-order interactions that are crucial for maintaining network integrity.
- A pathway to simplify complex network analysis by reducing non-essential interactions.
Conclusions:
- The proposed framework effectively quantifies redundancy in higher-order network structures.
- It facilitates the identification of essential interactions, simplifying complex system analysis.
- This approach enhances the interpretability and computational efficiency of higher-order network studies.
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