Optimal Identification of Multiple Diffusion Sources in Complex Networks with Partial Observations

Source localization is a typical inverse problem in complex networks, which is widely used in disease outbreak, rumor propagation and pollutants spread. In this paper, we propose that, based on network topology and the times at which the diffusion reached partial nodes, it is easy to identify the source. The results show that in six different networks, although the number of observers is small, the precision of source localization can be high. Precision increases with network size increasing and source number decreasing. Furthermore, our method makes the sources localization precision very robust, not only with the condition of three different given observers selection strategies, but with three various intensity noise on the diffusion path.