Influence of network structure on rumor propagation

Rumor propagation in complex networks is studied analytically and numerically by using the SIR model. Analytically, a mean-field theory is worked out by considering the influence of network topological structure and the unequal footings of neighbors of an infected node in propagating the rumor. It is found that the final infected density of population with degree k   is ρ(k)=1−exp(−αk)$\rho (k)=1-\exp (-\alpha k)$, where α is a parameter related to network structure. The number of the total final infected nodes depends on the network topological structure and will decrease when the structure changes from random to scale-free network. Numerical simulations confirm the theoretical predictions.