发表机构
Institute of Functional Biology and Genomics IBFG-CSIC; University of Salamanca（功能生物学与基因组学研究所（IBFG-CSIC）; 萨拉曼卡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文回应Peixoto等人关于图表达力的论点，指出超图被偏好的关键在于显式分离交互结构，并证明该表示一般对应有向超图，为高阶交互研究提供理论依据。
AI 中文摘要
Peixoto等人（arXiv:2602.16937v2）强调，基于图的表述可以表达任何交互模型，而高阶网络（HONs）领域的文献常常忽视这一点。我们同意他们批评中的大部分内容。然而，我们认为，表达力可能并不是超图常常被偏好的主要原因。网络是从模型中读取出来的，而非被假设出来的，为了恰当地研究结构的作用——这是复杂系统研究中最基本的问题之一——需要一种能够将结构保持在与交互函数形式分离的表示。我们表明，这种表示通常是一个有向超图（等价地，一个有向因子图），每个交互项对应一条超弧，对于成对交互可还原为（有向）图，对于对称的高阶交互则还原为无向超图。迄今为止，HONs文献大多集中于对称交互，鉴于本文所确立的结果，这可能解释了为何（无向）超图经常被呈现为具有高阶交互系统的自然表示。
英文摘要
Peixoto et al. (arXiv:2602.16937v2) stress that graph-based formulations can express any interaction model, a point the literature on higher-order networks (HONs) has often overlooked. We agree with much of their critique. We argue that expressiveness, however, might not be the main reason hypergraphs are often preferred. A network is read from a model rather than assumed, and to properly study the role of structure-one of the most basic questions in complex systems research-one needs a representation that keeps that structure separate from the functional form of the interactions. We show that such representation is in general a directed hypergraph (equivalently, a directed factor graph), with one hyperarc per interaction term, recovering a (directed) graph for pairwise interactions, and an undirected hypergraph for symmetric, higher-order ones. Most of the HONs literature has focused so far on symmetric interactions, which, in light of what established here, might explain why there (undirected) hypergraphs are regularly presented as the natural representation for systems with higher-order interactions.
Comments3 pages, 1 figure. Comment on 2602.16937v2. v2: clarified assumptions; corrected Eq. (6); minor edits
