Locating multi-source in time-varying networks with label back spread

The current sources localization mainly focuses on static network structures, however, the structure of real networks tends to change with time. Although great progress has been made in sources localization, how to locate the source in time- varying networks remains a challenge, especially when the spread dynamics model, the triggering time and the number of sources are unknown. Here we introduce a time aggregation graph (TAG) to characterize the time-varying network structure, and propose a reverse time aggregation graph (RTAG). Based on the RTAG, we introduce the idea of label back spread, and provide a convergent version and an iterative version of multi-source localization method for time-varying networks. The simulation results from synthetic networks and real social networks based on various spread dynamics models demonstrate that the proposed method is more accurate than two classical methods. What’s more, several interesting findings emerged from the research: (1) The presented approach can locate the source more accurately when there are more sources. (2) The proposed algorithm is robust to a variety of time-varying network topologies and propagation dynamics models. (3) Nodes frequently communicate with each other will benefit us to locate the source.