Impact of perception models on friendship paradox and opinion formation.

Topological heterogeneities of social networks have a strong impact on the individuals embedded in those networks. One of the interesting phenomena driven by such heterogeneities is the friendship paradox (FP), stating that the mean degree of one's neighbors is larger than the degree of oneself. Alternatively, one can use the median degree of neighbors as well as the fraction of neighbors having higher degree than oneself. Each of these reflects on how people perceive their neighborhoods, i.e., their perception models, hence how they feel the peer pressure. In our paper, we study the impact of perception models on the FP by comparing three versions of the perception model in networks generated with a given degree distribution and a tunable degree-degree correlation or assortativity. We numerically find that the network-level peer pressure is not necessarily negatively correlated with the assortativity in the case with the mean-based perception model. By simulating the opinion formation where the opinion adoption probability of an individual is given as a function of the individual peer pressure, we find that it takes the longest times to reach consensus when individuals adopt the median-based perception model, compared to other versions. Our findings suggest that one needs to consider the proper perception model for better modeling human behaviors and social dynamics.