Locating the propagation source in complex networks with observers-based similarity measures and direction-induced search.

Locating the propagation source is one of the most important strategies to control the harmful diffusion process on complex networks. Most existing methods only consider the infection time information of the observers, but the diffusion direction information of the observers is ignored, which is helpful to locate the source. In this paper, we consider both of the diffusion direction information and the infection time information to locate the source. We introduce a relaxed direction-induced search (DIS) to utilize the diffusion direction information of the observers to approximate the actual diffusion tree on a network. Based on the relaxed DIS, we further utilize the infection time information of the observers to define two kinds of observers-based similarity measures, including the Infection Time Similarity and the Infection Time Order Similarity. With the two kinds of similarity measures and the relaxed DIS, a novel source locating method is proposed. We validate the performance of the proposed method on a series of synthetic and real networks. The experimental results show that the proposed method is feasible and effective in accurately locating the propagation source.