# A Graph Convolutional Network-Based Method for Congested Link Identification
## 3 The GCN Approach
### Graph Structure Construction  
In Equation (11), \(P(y_{i}|p_{a}(y_{i}))\) can be obtained through Equation (12). However, the estimation of \(P(x_{j}|p_{a}(x_{j}))\) is hard in practice because it is difficult to accurately obtain the prior probabilities of channel cause congestion and node cause congestion. Inspired by the graph models, we propose a new approach based on the GCN to avoid any explicit estimation of these prior probabilities in the BNM (i.e., to use historical data to achieve the mapping between observations of end-to-end path states and unknown congestion links).  
We constructed a graph \(\mathbf{G}=(\
u,\varepsilon)\) for link congestion identification, where \(\
u\) is the set of nodes in the graph and \(\varepsilon\) represents the set of edges in the graph. There are three types of nodes in \(\
u\). The first type of node represents the route status, the second type of node represents the link status, and the third type of node represents the node status in the network. There are two types of edges in \(\varepsilon\). The edges between the link status nodes and route status nodes represent the routes which travel through the link, and the edges between the link status nodes and node status nodes represent the link starting from the node. We combined the route status node into two entities based on the test results. For example, if the test result is that the end-to-end path routes \(r_{3}\), \(r_{4}\), \(r_{5}\), \(r_{6}\), \(r_{7}\), and \(r_{8}\) are congested, and \(r_{1}\) and \(r_{2}\) are not congested, then the graph structure is constructed as shown in Figure 5.  
During the experimental process, we initially conducted multiple calculations and simulations based on the complete graph structure as shown in Figure 5, which included the route state nodes. However, upon observing and analyzing these results, we noticed that the route state nodes introduced a certain level of complexity during multiple iterations and calculations. This complexity not only increased the computation time but also potentially had subtle impacts on the accuracy of the results.  
To delve deeper into the reasons behind this observation, we conducted a comparative experiment, repeating the same calculations and simulations on a simplified graph which excluded all route state nodes. This alteration significantly simplified the graph structure, reducing the amount of data which needed to be processed.  
By comparing the results of the two experiments, we discovered that the graph without route state nodes was more efficient in terms of computation, and the stability and accuracy of the results were also enhanced. Specifically, we observed a substantial reduction in computation time and a narrowing of the fluctuation range of the results, making them closer to theoretical expectations.  
Given the experimental scenario, removing the route state nodes simplified the graph structure and improved the accuracy and efficiency of the calculation results. Consequently, based on this finding, we constructed the simplified graph shown in Figure 6 to carry out further analysis and research.  
In this way, we transformed the problem of link congestion identification into a node classification task as shown in Figure 7, where the link status nodes were categorized into two classes: congestion and normal.  
Figure 5: The graph constructed when \(r_{3}\), \(r_{4}\), \(r_{5}\), \(r_{6}\), \(r_{7}\), and \(r_{8}\) are congested.