How the node’s vital and tie strength effect rumor spreading on social network

The spread of rumors on complex networks has attracted wide attention in the field of management. In this paper, the generalized rumor spreading model is modified to take into account the vital of the spreader and the tie strength for the pairwise contacts between nodes in complex networks at degree-dependent spreading rate. Concretely, we introduce the infectivity exponent α, and the degree influenced real exponent β into the analytical rumor spreading model. Rumor infectivity, φ(k)=kα, where 0<α≤1, defines that each spreader node may contact kα neighbors within one time step. The tie strength between two nodes with degrees k and l are measured by ωkl=b(kl)β, β is the degree influenced real exponent which depends on the type of complex networks and b is a positive quantity. We use a tuning parameter θ to combine both the effect of the vital nodes and the strength of connectivity between nodes. We use analytical and numerical solutions to examine the threshold behavior and dynamics of the model on several models of social network. It was found that the infectivity exponent α, the degree influenced real exponent β and tuning parameter θ affect the rumor threshold, one can adjust the parameters to control the rumor threshold which is absent for the standard rumor spreading model.