Hyperedge overlap drives explosive transitions in systems with higher-order interactions
Federico Malizia1,2, Santiago Lamata-Otín3,4, Mattia Frasca5
1Network Science Institute, Northeastern University London, London, UK.
Nature Communications
|January 9, 2025
Summary
Higher-order interactions in complex systems drive novel behaviors. Microscopic organization, specifically low hyperedge overlap, is crucial for phenomena like abrupt transitions and bistability, not just the presence of these interactions.
Area of Science:
- Complex Systems Science
- Network Science
- Statistical Physics
Background:
- Collective behaviors in complex systems often arise from higher-order interactions.
- The precise influence of the microscopic organization of these interactions on system behavior remains unclear.
Purpose of the Study:
- To introduce a metric for quantifying hyperedge overlap in higher-order networks.
- To investigate the role of this overlap in dynamical processes like complex contagion and synchronization.
Main Methods:
- Quantification of intra-order hyperedge overlap in higher-order networks.
- Analysis of dynamical processes (complex contagion, synchronization) on networks with varying overlap structures.
Main Results:
- Real-world systems display diverse levels of intra-order hyperedge overlap.
- Intra-order hyperedge overlap universally influences collective behavior in complex contagion and synchronization.
- Abrupt transitions and bistability are contingent on low intra-order hyperedge overlap, not solely on higher-order interactions.
Conclusions:
- The microscopic structure of higher-order interactions, specifically hyperedge overlap, is a critical determinant of collective behavior.
- Achieving phenomena like explosivity and bistability necessitates specific network organizations with minimal overlap.
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