Effect of Contact Preference among Heterogeneous Individuals on Social Contagions

In social networks, individual heterogeneity is widely existed, and an individual often tends to contact more frequently with friends of similar status or opinion. It is worth noting that the contact preference characteristic among heterogeneous individuals will have a significant effect on social contagions. Thus, we propose a social contagion model which takes the heterogeneity of individual influence and contact preference into account, and make a theoretical analysis of the social spreading process by developing an edge-based compartmental theory. We find that the competition between simple contagion and complex contagion leads to the emergence of crossover phase transition phenomena when the influence of ordinary individuals is low: it changes from being hybrid to continuous, then to hybrid, and eventually to continuous phase transition with the increase of the contact probability of homogeneous individuals. However, it changes from being first-order to continuous phase transition when the influence strength of ordinary individuals is relatively high. In addition, there is an optimal value or range of contact probability of homogeneous individuals which maximizes the spreading size, and the optimal value or lower bound of the optimal range decreases with the increase of transmission probability. Our theoretical prediction results are in good agreement with the simulation results.