Accurate ranking of influential spreaders in networks based on dynamically asymmetric link weights

We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes [Formula: see text] and [Formula: see text] may differ in its importance for spreading from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text]. The key issue is whether node [Formula: see text] , after infected by [Formula: see text] through the edge, would reach out to other nodes that [Formula: see text] itself could not reach directly. It becomes necessary to invoke two unequal weights [Formula: see text] and [Formula: see text] characterizing the importance of an edge according to the neighborhoods of nodes [Formula: see text] and [Formula: see text]. The total asymmetric directional weights originating from a node leads to a novel measure [Formula: see text] , which quantifies the impact of the node in spreading processes. An [Formula: see text]-shell decomposition scheme further assigns an [Formula: see text]-shell index or weighted coreness to the nodes. The effectiveness and accuracy of rankings based on [Formula: see text] and the weighted coreness are demonstrated by applying them to nine real-world networks. Results show that they generally outperform rankings based on the nodes' degree and [Formula: see text]-shell index while maintaining a low computational complexity. Our work represents a crucial step towards understanding and controlling the spread of diseases, rumors, information, trends, and innovations in networks.