Relative betweenness centrality in complex networks

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 correlation 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 average cumulative probability distribution (CPD) of RBC follows a power law P(bₖ̄)~ bₖ̄-γ, where γ ≈ 1 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.