Using upper and lower bounds to estimate indirect influence probability in social networks under independent cascade model

Nowadays, popular social networks have become important media for many companies to conduct viral marketing, due to their low costs and high efficiencies for information diffusion. However, the fundamental problem of how to calculate the indirect influence probability between users who are not directly connected in social networks has not been well addressed, which is critical for problems like influence maximization and source detection. In this paper, to estimate this indirect influence probability under the independent cascade model, we propose two types of algorithms: the first type originates from Dijkstra’s algorithm, and the second type is based on graph compression. From these algorithms, we provide 4 lower and 2 upper bounds for the indirect influence probability. The performances of these bounds are investigated through computational experiments, from which we observe that the accuracies of some bounds may vary with propagation intensity, and the upper bounds seem to achieve better results than the lower ones. We believe that the findings in this paper can introduce new approaches for the indirect influence probability estimation problem and provide insights in understanding the diffusion dynamics in social networks.