Complex network centrality method based on multi-order K-shell vector

Abstract

The K-shell has important theoretical significance and application value in measuring the importance of nodes in complex networks. However, in the K-shell method, most of nodes possess an identical K-shell value so that the relative importance of the identical K-shell nodes cannot be further compared with each other. Therefore, based on the K-shell value of nodes in the complex network and the K-shell values of multi-order neighbors in complex networks, in this paper we use the vectors to represent the relative importance of node in each of complex networks, which is named multi-order K-shell vector. Multi-order K-shell vector centrality defines a vector indicating the number of multi-order neighbors with different K-shells and groups them into elements of the vector. Each vector infers to not only the original K-shell of the given node but also the number of its multi-order neighbors and their K-shell values, which indicates the propagation capability of the given node. An approach to comparing two multi-order K-shell vectors is also presented, which is used to sort the vectors to evaluate the node importance. The method is explored by comparing several existing centrality methods. Through the experiments of SI propagation and static attack experiments in seven real-world networks, it is found that multi-order K-shell vector centrality provides low computational complexity, effectively evaluates nodes with high propagation capability, which confirms the improved performance in susceptible infected model propagation experiments. On the other hand, the static attack experiments show that the multi-order K-shell vector tends to preferentially select the core structure with powerful propagation capability in the network. The multi-order K-shell vector greatly improves the difference rate of node centrality under the premise of preserving the K-shell structure information, as well as balancing the importance measure of nodes in the complex network and the structure evaluation of propagation capability. The multi-order K-shell vector is not appropriate for all types of networks when considering the result of network attacking. For the networks with low clustering coefficients and high average path lengths, multi-order K-shell vector method is dominant and the effect is relatively obvious. By contrast, multi-order K-shell vector surpasses most of centrality approaches when spreading information is our priority. In a few networks, eigenvector centrality presents a slightly better performance with a larger computational complexity. The proposed centrality measure is therefore of great theoretical and practical importance.