Effectively identifying multiple influential spreaders in term of the backward-forward propagation

Identification of multiple influential seed spreaders is one of the most promising domain in the research area of complex networks, which is also called the influence maximization problem in sociology domains. In order to evaluate the spreading ability of nodes in networks, many centrality-based indices have been proposed and achieved relatively good results. Although these methods can be directly applied to identify a set of important nodes via top-k strategy, an internal defect largely restricts the performance of them. In most networks, the important nodes often tend to distribute closely, leading to a severe influence overlapping problem which is harmful to their collective influence. In this paper, we propose a heuristic strategy, namely the backward-forward propagation, to sequentially select multiple decentralized yet influential seed spreaders. The first step is to estimate the probability of ordinary nodes being contacted by seed spreaders in the network via the backward propagation. Then we utilize the forward propagation to approximately evaluate the spreading ability of all the ordinary nodes, and select the one with the largest influence to be a new seed spreader. We conduct the numerical analysis on both undirected and directed networks, and the results all show that the proposed method can outperform several centrality-based and heuristic benchmarks. Specially, further analysis demonstrates the stability and adaptivity of our method.