# Cause Analysis and Accident Classification of Road Traffic Accidents Based on Complex Networks
## 3 Methodology
### Complex Network Evaluation Index  
The node evaluation index in complex networks is a specific representation of the topological relationship between nodes and edges in the network. Accurate analysis of the evaluation index can provide a better understanding of the characteristics of the network and the interaction between nodes [34]. In this paper, seven characteristic parameters, namely, degree of node, network diameter, average path length, clustering coefficient, intermediary centrality, closeness centrality, and comprehensive importance evaluation were selected as node indexes of complex networks for analysis, which can be seen in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Network Evaluation Index** & **Specific Description** \\ \hline Degree of node (\(D\)) & Indicates the number of edges by which a node \\  & connects to other nodes. \\ \hline Network diameter (\(S\)) & \begin{tabular}{c} Represents the maximum distance between any \\ two nodes. \\ \end{tabular} \\ \hline Average path length (\(L\)) & \begin{tabular}{c} Represents the average length of the shortest \\ path between all node pairs. \\ \end{tabular} \\ \hline Clustering coefficient (\(C\)) & \begin{tabular}{c} Indicates the degree of aggregation of the node \\ in the network \\ \end{tabular} \\ \hline Intermediary centrality (\(B\)) & \begin{tabular}{c} Indicates the adjustment ability and transfer \\ function of the node between other nodes. \\ \end{tabular} \\ \hline Closeness centrality (\(M\)) & \
\begin{tabular}{c} Indicates the proximity of the node to \\ other nodes \\ \end{tabular} \\ \hline Comprehensive importance evaluation (\(O\)) &
\begin{tabular}{c} Indicates the comprehensive importance of \\ nodes from a global perspective \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Node evaluation index of complex networks. (1) Degree of node \(D_{i}\), which represents the number of edges by which the node is connected to other nodes. The higher the degree of the node, the more significant the node is [35]. The calculation formula is shown as follows:  
\[D_{i}=\sum\limits_{j\in N}e_{ij} \tag{4}\]  
where \(D_{i}\) denotes the degree of a node and \(N\) denotes the number of nodes in the network, respectively. \(e_{ij}\) is the number of edges between nodes \(i\) and \(j\). (2) Network diameter \(S\), which represents the maximum distance between any two nodes in the network. The calculation formula is shown as follows:  
\[S=\underset{i,j\in N}{\max}\big{(}d_{ij}\big{)} \tag{5}\]  
where \(d_{ij}\) denotes the distance between nodes \(i\) and \(j\), which is expressed as \(d_{ij}=\sqrt{\big{(}x_{i}-x_{j}\big{)}^{2}+\big{(}y_{i}-y_{j}\big{)}^{2}}\). (3) Average path length \(L\), which indicates the average value of the distance between any two nodes in the network. The calculation formula is shown as follows:  
\[L=\frac{\sum\limits_{i\
eq j}d_{ij}}{\frac{1}{2}N(N-1)} \tag{6}\]  
(4) Clustering coefficient \(C_{i}\). It indicates the probability that two nodes adjacent to node \(i\) in the network are also adjacent, reflecting the level of clustering of nodes in the network. The larger the clustering coefficient, the closer the connection between nodes is [36]. The calculation formula is shown as follows:  
\[C_{i}=\frac{2E_{(i)}}{D_{i}(D_{i}-1)} \tag{7}\]  
where \(E_{(i)}\) denotes the number of edges that actually exist between node \(i\) and adjacent nodes. (5) Intermediary centrality \(B_{i}\). It refers to the shortest path number passing through the node, emphasizing the adjustment ability and transit function of the node between other nodes. Its normalized expression can be seen as follows:  
\[B_{i}=\frac{2\sum\limits_{s\
eq i\
eq t\in N}\frac{l_{s,t(i)}}{l_{s,t}}}{(N-1 )(N-2)} \tag{8}\]  
where \(l_{s,t}\) is the number of shortest paths between nodes \(s\) and \(t\), and \(l_{s,t(i)}\) is the number of shortest paths passing through node \(i\) between nodes \(s\) and \(t\). Nodes \(i\), \(j\), \(s\), and \(t\) denote any node in a complex network, and denote four independent nodes.