A rumor spreading pairwise model on weighted networks

The heterogeneity in edge weights plays a crucial role in the spread of a rumor on networks. To investigate the effects of weight distribution on a rumor spreading, we employ an ISR pairwise model on weighted regular random networks in this paper. The basic reproductive ratio of this model is derived, and it indicates that the heterogeneity in transmission rate leads to a fall in the basic reproductive ratio when the average transmission rate is fixed. Besides, by assuming that the transmission rate is a linear function of the edge weight, numerical simulation results of the model on networks with a bimodal weight distribution show that weight heterogeneity has a complex impact on the dynamics of a rumor. When we fix the proportions of two weights but vary their values to keep a constant average weight, increasing the heterogeneity in weight distribution slows down the initial growth rate, the final size and the maximum influence of a rumor, but increases the duration for rumor spreading. However, if we change both the values and proportions of two weights, only the mean and variance of the weight distribution are not able to provide sufficient information to predict the dynamics of a rumor. Moreover, we get similar simulation results in the case of nonlinear transmission rate. (C) 2021 Published by Elsevier B.V.

Automated summary

This study examines the role of edge weights in the spread of rumors on networks, finding that weight heterogeneity has complex effects on the dynamics of rumor propagation. Increasing weight distribution heterogeneity slows down the growth rate of rumors, decreases the final size and maximum influence, while increasing the duration of spreading. However, changes in both the values and proportions of weights make it difficult to predict the dynamics of rumors based solely on the mean and variance of weight distribution.