Effects of correlation between bounded confidences and node degrees on consensus in opinion dynamics on complex networks

In bounded confidence opinion dynamics, agents only consider other agents when their opinions are sufficiently close. In many works, the confidence bound is assumed as a homogeneous one. However, agents in different situations may be with different confidence bounds in real life. In this work, the correlation of degrees and confidence bounds is introduced into modified Hegselmann-Krause model on complex networks and we mainly focus on whether the population can reach consensus, where all agents hold a same opinion. The number of opinion clusters, the relative size of the largest cluster and the probability of reaching consensus are the measures of the opinion cluster profile. The numerical simulation shows that the existence of the correlation promotes the probability of reaching consensus and even in the case where some agents are with very small confidence bounds. On scale-free and Erdos-Renyi random networks, the negative correlation supports the consensus much more than the positive correlation case. However, two correlations show the same effect on small-world networks, and this effect is also observed in scale-free and Erdos-Renyi random networks when the average degree becomes very large.