标题：High-Order Degree and Combined Degree in Complex Networks
作者：Wang, Shudong; Wang, Xinzeng; Song, Qifang; Zhang, Yuanyuan
作者机构：[Wang, Shudong] China Univ Petr, Coll Comp & Commun Engn, Qingdao 266580, Peoples R China.; [Wang, Xinzeng; Song, Qifang] Shandong Univ Sci & Techno 更多
通讯作者地址：[Wang, XZ]Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266510, Peoples R China.
来源：MATHEMATICAL PROBLEMS IN ENGINEERING
摘要：We define several novel centrality metrics: the high-order degree and combined degree of undirected network, the high-order out-degree and in-degree and combined out out-degree and in-degree of directed network. Those are the measurement of node importance with respect to the number of the node neighbors. We also explore those centrality metrics in the context of several best-known networks. We prove that both the degree centrality and eigenvector centrality are the special cases of the high-order degree of undirected network, and both the in-degree and PageRank algorithm without damping factor are the special cases of the high-order in-degree of directed network. Finally, we also discuss the significance of high-order out-degree of directed network. Our centrality metrics work better in distinguishing nodes than degree and reduce the computation load compared with either eigenvector centrality or PageRank algorithm.