Influence propagation over large scale social networks

We study the influence diffusion problem in online social networks. Formally, given a network represented by a directed graph G = (V, E), we consider a process of influence diffusion in G that proceeds as follows: Initially only the vertices of a given S ⊆ V are influenced; subsequently, at each round, the set of influenced vertices is augmented by all the vertices in the network that have a sufficiently large number of already influenced incoming neighbors. The question is to find a small subset of vertices that can influence the whole network (target set). This is a widely studied problem that abstracts many phenomena in the social, economic, biological, and physical sciences. It is known to be hard to approximate within a factor of 2log1-εn, for any ε > 0, and n = |V|. Despite the above negative result, some efficient heuristics have been recently proposed in the literature. In this paper, we present a scalable, fast, and simple algorithm (MTS) for the influence diffusion problem. Experiments conducted over real-world social networks show that the proposed algorithm produces solutions that substantially outperform those obtained by previously published algorithms. Experiments also show that the performances of the analyzed algorithms (measured by the normalized target set size) correlates positively with the strength of communities of a network (measured by the network modularity). Such correlation is even stronger using the results provided by the MTS algorithm, showing that the proposed MTS algorithm better exploits situations in which the community structure of the networks allows some influence between different communities.