Integrated Network Vulnerability Assessment Using r-Power Entropy and Performance Metrics

In this article, we propose an integrated approach for network vulnerability and resilience assessment, combining graph theoretical methods with performance-based measures. Using rpower normalized entropy, which quantifies the complexity and randomness of the network’s structure by raising the adjacency matrix to the power of r, we analyze both the topological and weighted properties of the network. By simulating link failures and recalculating network performance (e.g., flows and load served), we assess the impact of disruptions, thereby quantifying the changes in entropy before and after the events, benchmarking the results against classic static metrics for links (e.g., betweenness centrality and closeness centrality). We synthesize these findings to identify critical links essential for maintaining network structure and performance. The analysis highlights key tradeoffs between structural entropy and real-world performance metrics, demonstrating that static indices have low correlation with operational loss, while the dynamic change in entropy successfully identifies latent, severe failures, providing a framework for network optimization and design. This methodology is applicable to networks where both structural integrity and resilience are vital (e.g., power grids, communication, and transportation). We use two real-world electric power system assessments to illustrate the value of the proposed methodology in gaining insights into the performance and vulnerability of power networks, even when only unweighted adjacency matrices are available.