Social contagions on time-varying community networks.

Time-varying community structures exist widely in real-world networks. However, previous studies on the dynamics of spreading seldom took this characteristic into account, especially those on social contagions. To study the effects of time-varying community structures on social contagions, we propose a non-Markovian social contagion model on time-varying community networks based on the activity-driven network model. A mean-field theory is developed to analyze the proposed model. Through theoretical analyses and numerical simulations, two hierarchical features of the behavior adoption processes are found. That is, when community strength is relatively large, the behavior can easily spread in one of the communities, while in the other community the spreading only occurs at higher behavioral information transmission rates. Meanwhile, in spatial-temporal evolution processes, hierarchical orders are observed for the behavior adoption. Moreover, under different information transmission rates, three distinctive patterns are demonstrated in the change of the whole network's final adoption proportion along with the growing community strength. Within a suitable range of transmission rate, an optimal community strength can be found that can maximize the final adoption proportion. Finally, compared with the average activity potential, the promoting or inhibiting of social contagions is much more influenced by the number of edges generated by active nodes.