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Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks
Hugo P Maia1, Wesley Cota1, Yamir Moreno2,3
1Departamento de Física, Universidade Federal de Viçosa, Viçosa, MG, Brazil.
Nature Communications
|July 15, 2026
Summary
We developed new algorithms to simulate complex systems with higher-order interactions, like social contagion. These methods significantly speed up simulations on large networks, making complex dynamics more accessible.
Area of Science:
- Complex Systems
- Network Science
- Computational Biology
Background:
- Higher-order interactions are crucial in complex systems but computationally challenging to simulate.
- Existing simulation methods face combinatorial complexity, limiting scalability.
Purpose of the Study:
- To develop efficient and statistically exact Gillespie algorithms for Markovian spreading dynamics on hypergraphs.
- To overcome computational bottlenecks in simulating higher-order interactions.
Main Methods:
- Developed novel Gillespie algorithms incorporating phantom processes.
- Achieved reduced computational complexity from O(N^2) to near-linear scaling.
- Utilized the susceptible-infected-susceptible model with critical mass thresholds for benchmarking.
Main Results:
- Algorithms demonstrate significant speedups (orders of magnitude) over standard approaches.
- Enabled simulations of networks with millions of nodes and high heterogeneity.
- Successfully addressed bottlenecks related to high interaction order and number.
Conclusions:
- Established a general framework for scalable, continuous-time simulations of higher-order contagion.
- The new algorithms facilitate the study of complex dynamics on large, heterogeneous hypergraphs.
- Opens avenues for research in neural, ecological, and social contagion dynamics.
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