# Cause Analysis and Accident Classification of Road Traffic Accidents Based on Complex Networks
## 4 Case Studies
### The Construction of a Road Traffic Accident Cause Analysis Network  
Taking the accidents' influencing factors and the severity of injury as nodes in the network, the relationships among influencing factors and the relationship between influencing factors and injury severity are regarded as the edge of the network. The steps are shown as follows:  
(1) The co-occurrence matrix A\({}_{1}\) is constructed as follows:  
\[\text{A}_{1}=\begin{bmatrix}\text{r}_{1}&\text{r}_{2}&\text{r}_{3}&\dots& \text{a}_{2}&\text{a}_{3}\\ \text{r}_{1}&0&0&128,441&\dots&233,527&2324\\ \text{r}_{2}&0&0&47,639&\dots&96,820&1462\\ \text{r}_{3}&128,441&47,639&0&\dots&52,903&614\\ \vdots&\vdots&\vdots&\vdots&\dots&\vdots&\vdots\\ \text{a}_{2}&233,527&96,820&52,903&\dots&0&0\\ \text{a}_{3}&2324&1462&614&\dots&0&0\end{bmatrix}\]  
where r\({}_{1}\)-r\({}_{47}\) represents the influencing factors of the accidents. a\({}_{1}\)-a\({}_{3}\) represent the severity of injury in the accidents.  
(2) According to the co-occurrence matrix A\({}_{1}\), the adjacency matrix A\({}_{2}\) is constructed as follows [41]. If there is a co-occurrence relationship between influencing factors and between influencing factors and injury severity, it is marked as 1, and if there is no co-occurrence relationship, it is marked as 0.  
\[\text{A}_{2}=\begin{bmatrix}\text{r}_{1}&\text{r}_{2}&\text{r}_{3}&\dots& \text{a}_{2}&\text{a}_{3}\\ \text{r}_{1}&0&0&1&\dots&1&1\\ \text{r}_{2}&0&0&1&\dots&1&1\\ \text{r}_{3}&1&1&0&\dots&1&1\\ \vdots&\vdots&\vdots&\vdots&\dots&\vdots&\vdots\\ \text{a}_{2}&1&1&1&\dots&0&0\\ \text{a}_{3}&1&1&1&\dots&0&0\end{bmatrix}\]  
(3) A Jaccard index matrix is constructed by A\({}_{1}\) and A\({}_{2}\) to describe the degree of correlation between nodes. The higher the co-occurrence rate, the higher the degree of association between the two nodes [42]. The Jaccard index matrix A\({}_{3}\) is shown below.  
\[\text{A}_{3}=\begin{bmatrix}\text{r}_{1}&\text{r}_{2}&\text{r}_{3}&\dots& \text{a}_{2}&\text{a}_{3}\\ \text{r}_{1}&0.000&0.000&0.164&\dots&0.280&0.003\\ \text{r}_{2}&0.000&0.000&0.118&\dots&0.190&0.005\\ \text{r}_{3}&0.164&0.118&0.000&\dots&0.117&0.003\\ \vdots&\vdots&\vdots&\vdots&\dots&\vdots&\vdots\\ \text{a}_{2}&0.280&0.190&0.117&\dots&0.000&0.000\\ \text{a}_{3}&0.003&0.005&0.003&\dots&0.000&0.000\\ \end{bmatrix}\]  
The complex network model for analyzing the causes of road traffic accidents is shown in Figure 3. The size of each node represents the relative weight. The larger the node, the more significant the factor it represents, while the thicker the edge, the stronger the connection between the two nodes. In this study, we simplify the complex network to  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Numbering** & **Severity of Injuries** \\ \hline a\({}_{1}\) & Ordinary accidents \\ a\({}_{2}\) & Serious accidents \\ a\({}_{3}\) & Major accidents \\ \hline \hline \end{tabular}
\end{table}
Table 3: Traffic accident injury severity type set.  
an undirected network, focusing on the relationship between the nodes rather than the directions of causality [43].