On the Effectiveness of Random Node Sampling in Influence Maximization on Unknown Graph

Influence maximization in a social network has been intensively studied, motivated by its application to so-called viral marketing. The influence maximization problem is formulated as a combinatorial optimization problem on a graph that aims to identify a small set of influential nodes (i.e., seed nodes) such that the expected size of the influence cascade triggered by the seed nodes is maximized. In general, it is difficult in practice to obtain the complete knowledge on large-scale networks. Therefore, a problem of identifying a set of influential seed nodes only from a partial structure of the network obtained from network sampling strategies has also been studied in recent years. To achieve efficient influence propagation in unknown networks, the number of sample nodes must be determined appropriately for obtaining a partial structure of the network. In this paper, we clarify the relation between the sample size and the expected size of influence cascade triggered by the seed nodes through mathematical analyses. Specifically, we derive the expected size of influence cascade with random node sampling and degree-based seed node selection. Through several numerical examples using datasets of real social networks, we also investigate the implication of our analysis results to influence maximization on unknown social networks.