The impact of the path ensemble on path percolation

Abstract

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.