Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [5], is a random process that takes values in the vertex set of a graph G, which is more likely to cross edges it has visited before. We show that it can be interpreted as an annealed version of the Vertex-reinforced jump process (VRJP), conceived by Werner and first studiedâ€¦Â (More)