Qiao Tong, Shan Wei, Yu Ganjun, Liu Chen
School of Economics and Management, Beihang University, Beijing 100191, China.
Key Laboratory of Complex System Analysis and Management Decision, Ministry of Education, Beijing 100191, China.
Entropy (Basel). 2018 Apr 9;20(4):261. doi: 10.3390/e20040261.
Measuring centrality has recently attracted increasing attention, with algorithms ranging from those that simply calculate the number of immediate neighbors and the shortest paths to those that are complicated iterative refinement processes and objective dynamical approaches. Indeed, vital nodes identification allows us to understand the roles that different nodes play in the structure of a network. However, quantifying centrality in complex networks with various topological structures is not an easy task. In this paper, we introduce a novel definition of entropy-based centrality, which can be applicable to weighted directed networks. By design, the total power of a node is divided into two parts, including its local power and its indirect power. The local power can be obtained by integrating the structural entropy, which reveals the communication activity and popularity of each node, and the interaction frequency entropy, which indicates its accessibility. In addition, the process of influence propagation can be captured by the two-hop subnetworks, resulting in the indirect power. In order to evaluate the performance of the entropy-based centrality, we use four weighted real-world networks with various instance sizes, degree distributions, and densities. Correspondingly, these networks are adolescent health, Bible, United States (US) airports, and Hep-th, respectively. Extensive analytical results demonstrate that the entropy-based centrality outperforms degree centrality, betweenness centrality, closeness centrality, and the Eigenvector centrality.
测量中心性最近引起了越来越多的关注，其算法范围从简单计算直接邻居数量和最短路径的算法到复杂的迭代细化过程和客观动力学方法。事实上，关键节点识别使我们能够理解不同节点在网络结构中所起的作用。然而，在具有各种拓扑结构的复杂网络中量化中心性并非易事。在本文中，我们引入了一种基于熵的中心性的新定义，它可适用于加权有向网络。通过设计，节点的总功率分为两部分，包括其局部功率和间接功率。局部功率可以通过整合结构熵（揭示每个节点的通信活动和受欢迎程度）和交互频率熵（表明其可达性）来获得。此外，可以通过两跳子网捕获影响传播过程，从而得到间接功率。为了评估基于熵的中心性的性能，我们使用了四个具有不同实例大小、度分布和密度的加权真实世界网络。相应地，这些网络分别是青少年健康网络、《圣经》网络、美国机场网络和高能物理理论（Hep-th）网络。大量分析结果表明，基于熵的中心性优于度中心性、介数中心性、接近中心性和特征向量中心性。
