Reevaluating Network Connectivity: The Critical Role of the Relative Size of Largest Connected Component (RSLCC)

In network structure analysis, metrics such as Isolated Node Ratio (INR), Network Efficiency (NE), Network Clustering Coefficient (NCC), Betweenness Centrality (BC), and Closeness Centrality (CC) are used as quantitative tools to measure network connectivity. However, there is another metric that is often easily overlooked and underestimated: the Relative Size of the Largest Connected Component (RSLCC). Our research not only proves that this metric is underestimated but also designs seven methods to predict its value, achieving a Deep Neural Network (DNN) prediction accuracy of more than 99%. DNN has demonstrated excellent predictive performance in large-scale networks, while Random Forest Regression (RFR) has proven to be highly effective and the fastest method for small-scale networks. The results of this research can be applied to any network. In a disaster scenario, whether it involves a physical network or a virtual abstract network. We illustrate the practical application of these insights using a case study of transportation network disaster rescue. Detailed steps are provided to explain how to implement these research findings in real-world scenarios, demonstrating the feasibility of applying this research to actual emergency situations.