Identifying influential nodes based on resistance distance

Nodes in a complex network are not all equally important. Depending on the purpose of the network, some nodes are considered more important, or more influential, more central, than the others. Identifying these influential, or central nodes, is a crucial issue, and of great significance not only for understanding the network's structural property, but also for its practical applications. Some commonly used measures to identify the influential nodes include Betweenness Centrality (BC), Closeness Centrality (CC), Degree Centrality (DC), Information Centrality (IC), Load Centrality (LC), Eigenvector Centrality (EC), and so on. In different contexts, various notions of distances have been used when a node's centrality is evaluated. In Brandes and Fleischer (2005), Brandes and Fleischer used resistance distance to calculate current-flow Betweenness Centrality (BCR) and current-flow Closeness Centrality (CCR). The resistance distance was used because it can more comprehensively reflect the communication cost between two nodes by taking into account all possible paths between them. Inspired by the work in Brandes and Fleischer (2005), in this paper we use resistance distance to calculate a group of resistive centralities including resistive Degree Centrality (DCR), resistive Eigenvector Centrality (ECR), resistive Harmonic Centrality (HCR), and resistive Eccentricity Centrality (ECCR). Based on the resistive centralities, we propose a new centrality ranking scheme named RCWTA, which hybridizes resistive centrality with classic centrality and weighted TOPSIS ranking method to identify influential nodes. Simulation experiments for 12 real-world networks are conducted and demonstrated to evaluate the effectiveness of the proposed resistive centrality measures. The experimental results indicate that all the resistive centrality measures outperform their corresponding classical counterparts except for ECR, with HCR showing the best performance.

Automated summary

Nodes in complex networks have different levels of importance. Identifying influential nodes is crucial for understanding the network's structure and practical applications. There are various measures to identify influential nodes, including Betweenness Centrality, Closeness Centrality, Degree Centrality, Information Centrality, Load Centrality, and Eigenvector Centrality. This paper proposes a new centrality ranking scheme named RCWTA, which combines resistive centrality with classic centrality and weighted TOPSIS ranking method. Simulation experiments show the effectiveness of the proposed resistive centrality measures, with resistive Harmonic Centrality performing the best.