Message passing approach for social contagions based on the trust probability with multiple influence factors

In social contagions, an individual to trust the behavioral information transmitted by neighbors depends on the level of the social status of neighbors as well as the closeness degree with neighbors. From the view of network topology, we propose the trust probability with multiple influence factors: node degree and the number of common neighbors. Furthermore, a weight factor is set to adjust the influence extent of the above two factors. As a result, in the context of the trust probability, we investigate social contagions with focus on social reinforcement and memory effect on networks, which are modeled by the threshold model. The message passing approach is adopted so as to formulate the state evolution of each node on the basis of network topology. Through extensive numerical simulations, we find that the trust probability can suppress social contagions, so does increasing the trust probability gap. Notably, the number of common neighbors as an influence factor of the trust probability is able to increase the final behavior adoption size, while node degree takes the opposite effect. The theoretical results are confirmed to agree well with the numerical results by the Monte Carlo method.