title: Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition.
abstract: Identifying the most influential spreaders is an important issue in understanding and controlling spreading processes on complex networks. Recent studies showed that nodes located in the core of a network as identified by the k-shell decomposition are the most influential spreaders. However, through a great deal of numerical simulations, we observe that not in all real networks do nodes in high shells are very influential: in some networks the core nodes are the most influential which we call true core, while in others nodes in high shells, even the innermost core, are not good spreaders which we call core-like group. By analyzing the k-core structure of the networks, we find that the true core of a network links diversely to the shells of the network, while the core-like group links very locally within the group. For nodes in the core-like group, the k-shell index cannot reflect their location importance in the network. We further introduce a measure based on the link diversity of shells to effectively distinguish the true core and core-like group, and identify core-like groups throughout the networks. Our findings help to better understand the structural features of real networks and influential nodes.
authors.affiliation: 1] Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China [2] School of Computer Science, Southwest Petroleum University, Chengdu 610500, China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Ming
authors.initials: M
authors.lastname: Tang
authors.affiliation: 1] Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China [2] Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Zhou
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea.
authors.lastname: Younghae Do