$\text {BC}_{\mathrm {DCN}}$: a new edge centrality measure to identify and rank critical edges pertaining to SIR diffusion in complex networks

Abstract

The identification of critical nodes and edges is essential for understanding the structural and functional aspects of complex networks. Like nodes, edges play a vital role in the structural organization of the complex systems and diffusion of the contagion. However, the identification of critical links traditionally has been given less attention compared to the identification of nodes. In this paper, we propose a new edge centrality measure derived from Betweenness Centrality, Degree, and Common Neighbourhood, namely $\text {BC}_{\mathrm {DCN}}$. Experimental analysis on a variety of networks shows that $\text {BC}_{\mathrm {DCN}}$ is capable of identifying those edges that facilitate Susceptible-Infected-Recovered (SIR) contagion diffusion. $\text {BC}_{\mathrm {DCN}}$ also shows good and non-degrading performance in experiments designed to study the effect on network size and connectivity under successive edge removal. Theoretically and empirically, the time complexity of $\text {BC}_{\mathrm {DCN}}$ is comparable to edge betweenness centrality, i.e., $\mathcal {O}(|E||V|)$. Unlike other measures, $\text {BC}_{\mathrm {DCN}}$ performs well on all three evaluation criteria, i.e., SIR diffusion simulation, successive edge removal experiments, and time complexity. It shows that the proposed method is fast and effective.