Hyperedge approximation for stochastic processes on higher-order networks
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911708369387520 |
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| author | Sheng, Anzhi McAvoy, Alex Tian, Ye Zhang, Silun Fontan, Angela Plotkin, Joshua B. |
| author_facet | Sheng, Anzhi McAvoy, Alex Tian, Ye Zhang, Silun Fontan, Angela Plotkin, Joshua B. |
| contents | Graphs are a standard framework for describing dynamical processes shaped by pairwise interactions among agents. But many systems involve interactions in groups of three or more agents. Here, we develop a method of "$\ell$-hyperedge approximation", a framework to analyze stochastic population processes on regular hypergraphs, in which each individual belongs to $k$ groups of size $\ell$. The framework accommodates both higher-order interactions that determine payoffs and higher-order processes for updating states in response to payoffs. Applied to evolutionary game dynamics, the framework generalizes the classical pairwise result on benefits and costs, $b/c>k$, that favors the spread of cooperation; and it provides critical benefit-to-cost ratios for nonlinear $\ell$-player public goods games that cannot be reduced to pairwise interactions. Applied to complex contagions, where inheritance of states occurs within hyperedges rather than along parent-offspring edges, the framework gives a closed-form result for the fixation probability, which shows how a complexity parameter governs the spread of rare types. Coupling the two processes produces a single stochastic model of payoff-biased complex contagion in structured populations. These results extend pair approximation from graphs to hypergraphs, accommodating multi-way interactions and inheritance structures with no pairwise analog. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23444 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyperedge approximation for stochastic processes on higher-order networks Sheng, Anzhi McAvoy, Alex Tian, Ye Zhang, Silun Fontan, Angela Plotkin, Joshua B. Physics and Society Biological Physics Graphs are a standard framework for describing dynamical processes shaped by pairwise interactions among agents. But many systems involve interactions in groups of three or more agents. Here, we develop a method of "$\ell$-hyperedge approximation", a framework to analyze stochastic population processes on regular hypergraphs, in which each individual belongs to $k$ groups of size $\ell$. The framework accommodates both higher-order interactions that determine payoffs and higher-order processes for updating states in response to payoffs. Applied to evolutionary game dynamics, the framework generalizes the classical pairwise result on benefits and costs, $b/c>k$, that favors the spread of cooperation; and it provides critical benefit-to-cost ratios for nonlinear $\ell$-player public goods games that cannot be reduced to pairwise interactions. Applied to complex contagions, where inheritance of states occurs within hyperedges rather than along parent-offspring edges, the framework gives a closed-form result for the fixation probability, which shows how a complexity parameter governs the spread of rare types. Coupling the two processes produces a single stochastic model of payoff-biased complex contagion in structured populations. These results extend pair approximation from graphs to hypergraphs, accommodating multi-way interactions and inheritance structures with no pairwise analog. |
| title | Hyperedge approximation for stochastic processes on higher-order networks |
| topic | Physics and Society Biological Physics |
| url | https://arxiv.org/abs/2605.23444 |