High-Order Degree and Combined Degree in Complex Networks

Abstract

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.

A New Method of Identifying Core Designers and Teams Based on the Importance and Similarity of Networks

“…Researchers have done a lot of work in this area and proposed many classic node importance evaluation algorithms [6], including Degree Centrality, Betweenness Centrality, Closeness Centrality, Eigenvector Centrality, and the K-shell decomposition algorithm [7][8][9][10][11]. In recent years, algorithms combining multiple attributes have emerged to measure the importance of nodes in complex networks.…”