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

TL;DR

This paper studies a coevolution model where node and link states evolve together with network topology changes, revealing a critical fragmentation transition and insights into social polarization.

Contribution

It introduces a coupled node-link dynamics model with rewiring, demonstrating a robust absorbing phase transition and network fragmentation at criticality, with implications for social systems.

Findings

Network fragmentation occurs at the critical line of the absorbing transition.

Finite-size fluctuations lead to a consensus phase in the active regime.

Survival time scales linearly with system size when rewiring occurs.

Abstract

We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such coevolution model features the interaction of the local dynamics of node and link states with the nonlocal dynamics of link-rewiring in a random network. The coupled dynamics of the states of the nodes and the links produces by itself an absorbing phase transition which is shown to be robust against the link rewiring mechanism. However, the dynamics of the network gives rise to significant physical changes, specially in the limit in which some links do not change state but are always rewired: First a network fragmentation occurs at the critical line of the absorbing transition, and only at this line, so that fragmentation is a manifestation of criticality. Secondly, in the active phase of the absorbing transition, finite-size fluctuations take the system to a single network component consensus phase, while other configurations are possible in the absence of rewiring. In addition, this phase is reached after a survival time that scales linearly with system size, while the survival time scales exponentially with system size when there is no rewiring. A social interpretation of our results contribute to the description of processes of emergence of social fragmentation and polarization.