Ranking spreaders by decomposing complex networks

Ranking the nodes' ability for spreading in networks is a fundamental problem which relates to many real applications such as information and disease control. In the previous literatures, a network decomposition procedure called k-shell method has been shown to effectively identify the most influential spreaders. In this paper, we find that the k-shell method have some limitations when it is used to rank all the nodes in the network. We also find that these limitations are due to considering only the links between the remaining nodes (residual degree) while entirely ignoring all the links connecting to the removed nodes (exhausted degree) when decomposing the networks. Accordingly, we propose a mixed degree decomposition (MDD) procedure in which both the residual degree and the exhausted degree are considered. By simulating the epidemic process on the real networks, we show that the MDD method can outperform the k-shell and the degree methods in ranking spreaders. Finally, the influence of the network structure on the performance of the MDD method is discussed.