2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166271It is shown that the path of a simple random walk on any graph, consisting of all vertices visited and edges crossed by the walk, is almost surely a recurrent subgraph.13 pages, updated version includes proof for unbounded degree graphs. Also see http://arxiv.org/abs/math/0603060 for another proofProbabilityMetric Geometry60G50text