Social Influence Maximization in Hypergraph in Social Networks

Crowd psychology plays an important role in determining the kind of activities that a person performs. In reality, in a social network, crowd influence has been observed and it cannot be ignored when considering information diffusion problems. In this paper, we model crowd influence as a hyperedge e = (H
_e
, v) with weight 0 ≤ P
_e
≤ 1, where H
_e
is the head node set and v is the tail node, means v will be activated by H
_e
with probability P
_e
only after each node in H
_e
is activated. Then, the Social Influence Maximization Problem in Hypergraph (SIMPH) aims to select k initially-influenced seed users in a directed hypergraph G = (V, E, P). The objective is to maximize the expected number of eventually-influenced users. We show that SIMPH is NP-hard and the objective function is neither submodular nor supermodular. We develop a lower bound and an upper bound that are submodular. We prove that maximizing these two bounds are still NP-hard under IC model. Then, we present a D-SSA algorithm for general weighted social influence maximization problem preserving (1 - 1=e - ε)-approximation. We formulate a sandwich approximation framework, which preserves a theoretical analysis result. Finally, we evaluate our algorithm on real world data sets. The results show the effectiveness and the efficiency of the proposed algorithm.