发表机构
Advanced-Basic-Convergence Research Institute, Chungbuk National University; Department of Physics, Chungbuk National University; Centre for Complex Systems, School of Mathematical Sciences, Queen Mary University of London（忠北国立大学先进基础融合研究院; 忠北国立大学物理系; 伦敦大学玛丽女王学院数学科学学院复杂系统中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出带锚节点的超图$(k,n)$-核心渗流理论框架，推导两类剪枝过程自洽方程，绘制含两类相变的相图，经数值模拟验证，揭示节点角色异质性与相互作用范围对高阶网络鲁棒性的影响。
AI 中文摘要
超图描述涉及两个以上节点的高阶相互作用，其特征在于鲁棒性会受节点不同角色的强烈影响：部分节点对超边功能至关重要，其他节点则非必需；单个必需节点的缺失会完全破坏其所属超边，而非必需节点的缺失则产生缓冲效应，使超边仅缩小规模。为刻画该现象，本文构建超图上$(k,n)$-核心渗流模型的综合理论框架：超边中每个节点以概率$\theta$为锚节点，超边失效当且仅当其锚节点失效。超图$(k,n)$-核心渗流问题可分为第一邻居问题与第二邻居问题，分别对应剪枝过程中连通性仅由第一邻居或第二邻居的状态保证。本文推导了第一邻居和第二邻居（基于节点与超边）剪枝过程的自洽方程，得到巨型$(k,n)$-核心的尺寸，绘制包含连续相变与不连续相变的相图，并通过随机超图上的数值模拟验证理论。结果表明，节点功能角色的异质性与相互作用的扩展范围如何影响高阶网络的鲁棒性。
英文摘要
Hypergraphs describe higher-order interactions that involve more than a pair of nodes. A characteristic feature of hypergraphs is that their robustness can be strongly affected by the different roles of the nodes. Indeed, some nodes might be essential for a hyperedge's function, while others might not be. The loss of a single essential node completely destroys the hyperedge it belongs to, while the loss of a non-essential node has a buffering effect, inducing the hyperedge to simply reduce its size. In order to capture this phenomenology, we formulate a comprehensive theoretical framework for $(k,n)$-core percolation models on hypergraphs, where each node of a hyperedge is an anchor with probability $θ$, and a hyperedge fails if an anchor node fails. Hypergraph $(k,n)$-core percolation problems can be classified as first-neighbor and second-neighbor problems, indicating that in the pruning process the connectivity is ensured only by the state of the first neighbors or the second neighbors, respectively. We derive self-consistency equations for first-neighbor and second-neighbor (node- and hyperedge-based) pruning processes, and obtain the size of the giant $(k,n)$-core. We obtain the phase diagram, including continuous and discontinuous transitions, and confirm our theory on random hypergraphs using numerical simulations. The results show how the heterogeneity of the nodes' functional roles and the extended range of the interactions affect the robustness of higher-order networks.
Comments11 pages, 5 figures
