  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 i and j may
differ in its importance for spreading from i to j and from j to i. The key
issue is whether node j, after infected by i through the edge, would reach out
to other nodes that i itself could not reach directly. It becomes necessary to
invoke two unequal weights wij and wji characterizing the importance of an edge
according to the neighborhoods of nodes i and j. The total asymmetric
directional weights originating from a node leads to a novel measure si which
quantifies the impact of the node in spreading processes. A s-shell
decomposition scheme further assigns a s-shell index or weighted coreness to
the nodes. The effectiveness and accuracy of rankings based on si 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 k-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.
