Source localization in signed networks with effective distance

While progress has been made in information source localization, it has overlooked the prevalent friend and adversarial relationships in social networks. This paper addresses this gap by focusing on source localization in signed network models. Leveraging the topological characteristics of signed networks and transforming the propagation probability into effective distance, we propose an optimization method for observer selection. Additionally, by using the reverse propagation algorithm we present a method for information source localization in signed networks. Extensive experimental results demonstrate that a higher proportion of positive edges within signed networks contributes to more favorable source localization, and the higher the ratio of propagation rates between positive and negative edges, the more accurate the source localization becomes. Interestingly, this aligns with our observation that, in reality, the number of friends tends to be greater than the number of adversaries, and the likelihood of information propagation among friends is often higher than among adversaries. In addition, the source located at the periphery of the network is not easy to identify. Furthermore, our proposed observer selection method based on effective distance achieves higher operational effciency and exhibits higher accuracy in information source localization, compared with three strategies for observer selection based on the classical Full-order neighbor coverage.