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Individuals who interact with each other in social networks often exchangeideas and influence each other's opinions. A popular approach to study thespread of opinions on networks is by examining bounded-confidence models(BCMs), in which the nodes of a network have continuous-valued states thatencode their opinions and are receptive to other nodes' opinions when they liewithin some confidence bound of their own opinion. In this paper, we extend theDeffuant--Weisbuch (DW) model, which is a well-known BCM, by examining thespread of opinions that coevolve with network structure. We propose an adaptivevariant of the DW model in which the nodes of a network can (1) alter theiropinions when they interact with neighboring nodes and (2) break connectionswith neighbors based on an opinion tolerance threshold and then form newconnections following the principle of homophily. This opinion tolerancethreshold determines whether or not the opinions of adjacent nodes aresufficiently different to be viewed as `discordant'. Using numericalsimulations, we find that our adaptive DW model requires a larger confidencebound than a baseline DW model for the nodes of a network to achieve aconsensus opinion. In one region of parameter space, we observe`pseudo-consensus' steady states, in which there exist multiple subclusters ofan opinion cluster with opinions that differ from each other by a small amount.In our simulations, we also examine the importance of early-time dynamics andnodes with initially moderate opinions for achieving consensus. Additionally,we explore the effects of coevolution on the convergence time of our BCM.

An Adaptive Bounded-Confidence Model of Opinion Dynamics on Networks