AI 中文总结
该研究引入广义路径渗流框架，发现有限路由 horizon 下过程粗粒化为平均场渗流，负载熵是网络鲁棒性度量，还识别出路径延长为基础设施故障前兆，明确了微观路由组织对宏观弹性的影响。
AI 中文摘要
从通信网络中的丢包到交通系统的拥堵崩溃，由流量引发的故障发生于流逐步耗尽其经过的边时。路径渗流通过沿采样的源-目的地路径移除边来建模这一过程。现有研究假设网络为局部树状且采用确定性最短路径路由，这使得路径简并性和路由随机性如何影响真实系统中典型的聚类网络的碎片化仍不明确。我们引入了一个广义路径渗流框架，其中路径来自温度控制的路由集合，在测地线与噪声传输之间插值。基于盒覆盖重整化和我们的数值实验，我们指出，对于任意有限的路由 horizon C，该过程粗粒化为普通平均场渗流。路由细节通过负载分布的熵和有限集群容纳流的能力影响非普适量，尤其是渗流阈值 p_c。因此，负载熵可作为基于路径的故障下网络的鲁棒性度量。当路由 horizon 被调整为平均场相关长度 C=N^{1/3}，且在源均匀集合内时，系统进入交叉 regime，其标度指数不同于无限预算的最短路径渗流。在该 regime 中，路径延长在时间上与结构解耦：特征路径长度达到与路由温度相关的增长最大值，且渐近于巨型组件崩溃之前。这些结果阐明了微观路由组织如何塑造宏观弹性，并确定路径延长为通信和交通基础设施故障的可测量前兆。
英文摘要
Traffic-induced failures, from packet loss in communication networks to congestion breakdown in transport systems, occur when flows progressively exhaust the edges they traverse. Path percolation models this process by removing edges along sampled origin-destination paths. Existing work assumes locally tree-like networks and deterministic shortest-path routing, leaving unclear how path degeneracy and routing stochasticity affect fragmentation in the clustered networks typical of real systems. We introduce a generalised path-percolation framework where paths are drawn from a temperature-controlled routing ensemble interpolating between geodesic and noisy transport. We argue based on box-covering renormalisation and our numerical experiments that, for any finite routing horizon $C$, the process coarse-grains to ordinary mean-field percolation. Routing details affect non-universal quantities, especially the percolation threshold $p_c$, through the entropy of the load distribution and the capacity of finite clusters to accommodate flow. Load entropy therefore acts as a robustness measure for networks under path-based failures. When the routing horizon is tuned to the mean-field correlation length, $C=N^{1/3}$, within a source-uniform ensemble, the system enters a crossover regime with scaling exponents distinct from shortest-path percolation with infinite budget. In this regime, path elongation becomes decoupled in time from structural fragmentation: the characteristic path length reaches a growing maximum, associated with routing temperature, asymptotically ahead of the collapse of the giant component. These results clarify how microscopic routing organisation shapes macroscopic resilience, and identify path elongation as a measurable precursor of failure in communication and transport infrastructure.
Comments24 pages, 9 figures, includes Supplementary Material
