# A Research Approach to Port Information Security Link Prediction Based on HWA Algorithm
## 3 Preliminaries
### Graph Convolutional Networks  
The core of graph convolutional networks (GCNs) [25] is to extract spatial features of graph structures. Viewing the port information dissemination network as a graph structure helps to systematically analyze and understand the information flow and interaction relationships between ports. Through graph convolutional networks (GCNs), a series of operations can be effectively performed on this graph structure. A GCN is similar to traditional convolution operations, where graph convolution filters waves on the graph to extract feature representations of nodes. The difference is that GCNs do not rely on fixed-size local neighborhoods when considering neighbor information but focus on the structure of the entire graph. The information between nodes propagates through the edges of the graph. Through matrix multiplication and activation functions, each node can aggregate information from its neighboring nodes to update its own representation. A GCN is a multilayer graph convolutional neural network, where each layer only processes information from the first-order neighborhood. By stacking multiple convolutional layers, information transfer between higher-order neighborhoods can be achieved. This article proposes a GCN method that utilizes the topology of graph structures to comprehensively consider the information of each node and its neighboring nodes. It can capture complex high-order associations between ports, which helps to comprehensively understand the complexity of port information security and improve the ability to identify complex network structures.  
Starting from the input layer, the forward propagation goes through the operation of the graph convolution layer followed by the operation of the softmax activation function to  
Figure 1: Schematic diagram of graph and hypergraph.  
obtain the predicted classification probability distribution. The computation of the graph network is an iterative process that constantly considers the neighboring nodes and the features of node, and each iteration is a feature reorganization, i.e., the next layer of features for the previous layer of features of the graph convolution (1) [26], that is, the propagation between the layers:  
\[X^{l+1}=\sigma\big{(}D^{\sim-\frac{1}{2}\sim\sim\sim-\frac{1}{2}}X^{l}W^{l} \big{)} \tag{1}\]  
\(X^{l+1}\) in Equation (1) is the feature matrix of the \(l+1\) th layer, and \(\sigma\) is the activation function. When calculating the new node features, not only the information of the neighboring nodes but also the information of its nodes can be taken into account, so the representation on the adjacency matrix \(A\) is \(\overset{\sim}{A}=A+I\), where \(I\) is the unit array. Similarly, for the degree matrix \(D\), not only the number of neighboring nodes but also their own information should be taken into account. Therefore, the unit array \(I\) is added to the degree matrix \(D\), the sum of each row of \(\overset{\sim}{A}\), \(\overset{\sim}{D}=D+I=\sum_{j}\overset{\sim}{A_{ij}}\) and \(\overset{\sim}{A_{ij}}\) to represent the elements of the \(i\) rows and \(j\) columns in \(\overset{\sim}{A}\). The matrix after matrix normalization is \(\overset{\wedge}{A}\), as shown in Equation (2):  
\[\overset{\wedge}{A}=\overset{\sim}{D}^{-\frac{1}{2}}\overset{\sim}{A}\overset {\sim}{D}^{-\frac{1}{2}} \tag{2}\]  
The new reorganization characteristics at this point are shown in Equation (3):  
\[X^{l+1}=\sigma\big{(}\overset{\wedge}{A}X^{l}W^{l}\big{)} \tag{3}\]  
Then, the forward propagation equation for a two-layer GCN network is shown in Equation (4), where \(\sigma\) and softmax are the activation functions:  
\[Z^{l+1}=softmax\bigg{[}\sigma\big{(}\overset{\wedge}{A}X^{l}W^{l}\big{)}\bigg{]},I=0,1 \tag{4}\]