Social contagion with degree-dependent thresholds

We investigate opinion spreading by a threshold model in a situation where the influence of people is heterogeneously distributed. We focus on the response of the average opinion as a function between the trend between out-degree (number of neighbors)---effectively the strength of influence of a node---and the threshold for adopting a new product or opinion. We find that if the coupling is very positive, the final state of the system will be a mix of different opinions otherwise it will it converges to a consensus state. We find that this cannot be simply explained as a phase transition, but emerges from a combination of mechanisms and their relative dominance in different regions of parameter space.