Relative betweenness centrality in complex networks

¹ Guangzhou College of Technology and Business - Guangzhou 5610850, PRC
² University of Electronic Science and Technology of China Zhongshan Institute - Zhongshan 528402, PRC
³ Foshan University - Foshan 528225, PRC

Received: 4 May 2025
Accepted: 20 October 2025

Abstract

Measuring the importance of nodes is a fundamental approach for understanding and governing the functionality of complex networks. So far, the majority of methods for quantifying node importance concentrate on their impacts on the global functionality of networks, ignoring the internal correlations among network nodes. To this end, this letter proposes the concept of Relative Between Centrality (RBC), which can quantify the load correlations among nodes in information transmission. Furthermore, we prove that the Cumulative Probability Distribution (CPD) of average RBC denoted by follows a power law , where for networks with an arbitrary degree distribution, indicating that such a probability distribution is a universal behavior in the network world. Finally, we employ RBC to control cascading failures in complex networks. Specifically, we propose two strategies —IR-RBC (RBC-based Intentional Removal) and TL-RBC (RBC-based Traffic Limiting)—to mitigate cascading failures in scale-free networks. The simulation results confirm the effectiveness of the proposed strategies.