Opinion dynamics in networks with common-neighbors-based connections

We investigate opinion dynamics of the model in which each agent can communicate with local neighbors whose opinions are inside the bound of confidence and meanwhile selecting long-range neighbors according to a common-neighbors rule. The common-neighbors rule means that two agents sharing more neighbors have larger probability to be connected. We find that increasing communication between agents who have common friends will prolong the time needed for the system to reach a consensus state. In contrast, the long-range connections between agents sharing no friends will promote the convergence of the system. The generality of this observation is tested against different system sizes. Simulation results also show that a large number of long-range connections help the system to reach a consensus fast.