Paper Overview
Hyperedge Approximation for Stochastic Processes on Higher-Order Networks
Takeaway: The paper develops an edge approximation for stochastic processes on hypergraphs. The framework accommodates higher-order interactions both in the payoff-generating phase (evolutionary games on hypergraphs) and also in the state updating phase (complex contagion).
Why It Matters
Many biological and social systems cannot be fully understood through pairwise interactions alone. Growing evidence shows that emerging phenomena often arise from higher-order interactions involving groups of three or more nodes, which cannot be adequately represented by pairwise graphs.
Examples: multiple species compete for food, territory, or other resources; face-to-face human communication; chemical reaction systems; gene regulatory networks; and brain networks.
Technical Contribution
- Develop a method of "ℓ-hyperedge approximation", a framework to analyze stochastic population processes on regular hypergraphs.
- Handles higher-order interactions in both payoff generating and state updating.
- Applied to evolutionary games, the framework generalizes the classical pairwise result. It also provides critical benefit-to-cost ratios for public goods games that cannot be reduced to pairwise interactions.
- Applied to complex contagions, the framework gives a closed-form result for the fixation probability.
Who Should Read This
Researchers in hyper-networked systems, evolutionary games, stochastic population processes, cooperation, complex contagion, network science, and collective decision-making.
Links
@misc{sheng2026hyperedge,
title = {{Hyperedge approximation for stochastic processes on higher-order networks}},
author = {Sheng, A. and McAvoy, A. and Tian, Y. and Zhang, S. and Fontan, A. and Plotkin, J. B.},
year = {2026},
eprint = {2605.23444},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.23444}
}