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We consider a general model in which there is a coupled dynamics of nodestates and links states in a network. This coupled dynamics coevolves withdynamical changes of the topology of the network caused by a link rewiringmechanism. Such coevolution model features the interaction of the localdynamics of node and link states with the nonlocal dynamics of link-rewiring ina random network. The coupled dynamics of the states of the nodes and the linksproduces by itself an absorbing phase transition which is shown to be robustagainst the link rewiring mechanism. However, the dynamics of the network givesrise to significant physical changes, specially in the limit in which somelinks do not change state but are always rewired: First a network fragmentationoccurs at the critical line of the absorbing transition, and only at this line,so that fragmentation is a manifestation of criticality. Secondly, in theactive phase of the absorbing transition, finite-size fluctuations take thesystem to a single network component consensus phase, while otherconfigurations are possible in the absence of rewiring. In addition, this phaseis reached after a survival time that scales linearly with system size, whilethe survival time scales exponentially with system size when there is norewiring. A social interpretation of our results contribute to the descriptionof processes of emergence of social fragmentation and polarization.

Absorbing transition in a coevolution model with node and link states in an adaptive network: Network fragmentation transition at criticality