Assessing Robustness and Vulnerability in Interdependent Network Infrastructure: A Multilayer Network Approach

Modern societies profoundly depend upon interdependent critical infrastructure systems, such as the power grid, oil pipeline, gas pipeline, and transportation system, for proper functioning. These systems are extensively interconnected, characterized by their interconnected layers of infrastructures, which presents unique complexities that can complicate their analysis. Furthermore, if one system fails, it can have a ripple effect throughout the entire network. Hence, it is crucial to evaluate the robustness and vulnerability of interdependent critical infrastructure systems with complex inter-layer and intra-layer dependencies to ensure their continued operation and after-math resilience. In response to these challenges, this study presents a method for evaluating the robustness, vulnerability, and efficiency of multi-layer infrastructures using various probabilistic evaluation measures. We considered three key parameters: the number of nodes (N), the denseness of network connections (DL), and node failure probability (p). We modeled these complex systems using Erdos-Renyi graphs and investigated the impact of three parameters: N, DL, and p. We considered two network sizes, N = 50 and N = 100, each divided into two layers with equal nodes. The DL and $p$ parameters represent the distinct characteristics of different infrastructures, which are considered independently for each layer. We simulated four scenarios varying DL and $p$ across layers and examined the topological transformations induced by these variations. The results indicated that a larger network size generally enhances network robustness and efficiency while reducing vulnerability, highlighting the importance of considering network size in multi-layer network design. Also, the interplay between DL and $p$ significantly influences network behavior, with a high DL mitigating the impact of high node failure probabilities on network robustness. These insights offer valuable guidelines for improving network resilience against potential node failures and are crucial for infrastructure designers and network analysts.