We study a coevolution voter model on a network that evolves according to the state of the nodes. In a single update, a link between opposite-state nodes is rewired with probability p, while with probability 1−p one of the nodes takes its neighbor’s state. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value p_c=(µ-2)/(µ-1) that only depends on the average degree μ of the network. The approach to the final state is characterized by a time scale that diverges at the critical point as |p_c-p|^-1 . We find that the active and frozen phases correspond to a connected and a fragmented network respectively.  We show that the transition in finite-size systems can be seen as the sudden  change in the trajectory of an equivalent random walk at the critical rewiring rate p_c, highlighting the fact that the mechanism behind the transition is a competition between the rates at which the network and the state of the nodes evolve.

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