Rumor spreading in a dual-relationship network with diverse propagation abilities

The increasing number of online ties created on social platforms has made our social relations and influences more complex and diverse. This paper proposes a multilayer-like network model for rumor spreading that incorporates both strong and weak relations. Two types of fixed topologies are used to describe strong relations, while the activity-driven model is employed for weak relations. The model also takes into consideration the differential propagation abilities of individuals. The rumor spreading thresholds are theoretically derived using mean-field theory and an approximation method, which are consistent with simulation results. Results indicate that differences in individuals’ strong relations significantly influence rumor spreading. Specifically, when the strong relation structure is a heterogeneous network, the density of rumor spreaders reaches equilibrium in a shorter time, and the final density of rumor spreaders is higher. However, when the strong relation structure is a homogeneous network and individuals’ activity rates are negatively correlated with their propagation abilities, rumor spreading is easier. Interestingly, the opposite result is obtained when the strong relation structure is a heterogeneous network. Additionally, individuals’ propagation abilities and weak relations can affect the final density of rumor spreaders, but the effects are not identical.