## 3 Materials and Methodology
### Development of a Modeling Framework to Estimate Traffic Volume  
To assess the impact of critical-link attacks on traffic volume, a modeling framework was developed. Here, the traffic volume is considered the response variable, and the topological parameters utilized in this study are considered the explanatory variables. To obtain more reliable and precise model results, the CMA was considered for model development because it incorporates more road segments than the study area. The final dataset comprised a road network with 638 road segments, each including its respective traffic volume and topological parameter values. For feature selection, we conducted a correlation coefficient assessment, and the explanatory variables greater than \((r\geq\pm 0.6)\) were selected for model development. This approach has been commonly used in previous studies on feature selection in transportation research [51]. This study employed a multiple linear regression model for model formulation. According to the correlation assessment results of each feature variable with traffic volume, there were distinct positive relationships, ranging from very to moderately to strongly positive correlations for SC (\(r=0.817,\ p<.01\)), BC (\(r=0.790,\ p<.01\)), EC (\(r=0.665,\ p<.01\)), and CC (\(r=0.523,\ p<.01\)). Among them, the SC and BC feature variables are distinguished by a strong positive correlation, and the EC variable is distinguished by a moderately strong positive correlation. However, CC showed a moderately positive correlation. Therefore, SC, BC, and EC were selected as feature variables, considering their greater correlation with traffic volume. Hence, the model comprising SC, BC, and EC explanatory variables was considered an acceptable model with which to assess traffic volume changes under critical-link attacks. Hence, the traffic volume of a given topological segment can be expressed as follows:  
\[TV_{i}=a+b\cdot SC_{i}+c\cdot BC_{i}+d\cdot EC_{i} \tag{6}\]  
where \(TV_{i}\) is the traffic volume of road segment \(i\). \(SC_{i}\) is the street connectivity of road segment \(i\). \(BC_{i}\) is the betweenness centrality of road segment \(i\). \(EC_{i}\) is the eigenvector centrality of road segment \(i\). \(a\), \(b\), \(c\), and \(d\) are constant values. In considering the model comprising coefficient values, SC (coefficient: 64.220, \(p<0.0001\)), BC (coefficient: 51.935, \(p<0.0001\)), and EC (coefficient: 31.295, \(p<0.0001\)) were all significant predictors of the dependent variable in the multiple linear regression model, as shown in Table 1, which depicts the statistics and specifications of the proposed model. Each of these variables had a positive influence on the dependent variable, with higher values associated with larger changes in the dependent variable. Thus, the SC and BC variables significantly influenced traffic volume prediction compared to the EC variable of the model. Additionally, the extremely low \(p\)-values for each independent variable indicated that the coefficient was statistically significant at an extremely high level (less than 0.01%). This suggests that each independent variable strongly influences the dependent variable in the model. Subsequently, the selected variables were assessed for the presence of multicollinearity. Multicollinearity refers to the phenomenon in which two or more predictor variables in a regression model are highly correlated, making it difficult to distinguish the independent effects of each variable on the outcome variable [52]. We used two methods to detect the presence of multicollinearity: the variance inflation factor (VIF) and tolerance. The VIF measures the extent to which the variance of a regression coefficient is inflated due to multicollinearity with other predictor variables. A VIF greater than 5 or 10 is often considered indicative of problematic multicollinearity [53]. Conversely, tolerance is defined as the proportion of variance in a predictor variable that is not explained by other predictor variables in the model.