## 2 Materials and Methods
### The Label of the GBNSS Model  
Network alignment seeks to identify analogous elements between two networks, such as biological pathways. Topological measurement indices evaluate the quality of network alignment. The definitions of three widely used network alignment metrics, EC, LCCS, and S3, are detailed as follows:  
* Edge Correctness (EC): _EC_ is a quantitative measure that assesses the degree of edge alignment between two networks based on a node mapping [32], and provides insight  
Figure 1: Node-level features and graph-level features.  
into the structural similarity and accuracy of mapping between the two networks. The EC is defined as  
\[EC(P,Q)=\frac{|\{(u,v)\in E_{1}\wedge(f(u),f(v))\in E_{2}\}|}{min(|E_{1}|,|E_{2}| )}, \tag{1}\]  
where \(E_{1}\) and \(E_{2}\) are the set of edges in network \(P\) and \(Q\), respectively. \(u\) and \(v\) are nodes in network \(P\); \(f(u)\) and \(f(v)\) are the corresponding nodes in network \(Q\) that \(u\) and \(v\) are mapped to. \(min(|E_{1}|,|E_{2}|)\) takes the minimum of the number of edges in \(P\) and \(Q\). The EC value ranges from 0 to 1, where 1 signifies complete overlap and 0 indicates no overlap at all. A higher EC value generally indicates a greater overlap of edges between the two networks after mapping, which typically suggests a higher degree of structural similarity between them.
* Largest Common Connected Subgraph (LCCS): LCCS is the largest subgraph that is shared between two or more graphs, where the subgraph is both connected and identical in terms of its nodes and edges across the graphs. It is calculated by counting the edges in the largest connected subgraph between two networks [33]. A larger and denser subgraph reflects the network's topological importance. LCCS is used to avoid problems with high Edge Count (EC) scores that may not necessarily reflect a connected substructure. In the case of two different alignments with the same EC score, the alignment with a higher LCCS is better.
* Symmetric substructure score (S3): S3 effectively measures how well edges are conserved in a global network alignment [17] and has been shown to be a superior metric for comparing sparser network regions to denser ones, unlike EC. The S3 is defined as follows: \[S3(P,Q)=\frac{|\{(u,v)\in E_{1}\wedge(f(u),f(v))\in E_{2}\}|}{|E_{1}|+|E(Q[f( V_{1})])|-|\{(u,v)\in E_{1}\wedge(f(u),f(v))\in E_{2}\}|},\] (2) where \(|E_{1}|\) is the total number of edges in the network \(P\); \(V_{1}\) is the set of nodes in the network \(P\). \(E(Q[f(V_{1})])\) denotes the edges in the graph of network \(Q\) induced by \(f(V_{1})\), which are the edges between the images of the nodes in \(V_{1}\) under the mapping \(f\). A higher S3 indicates a greater degree of symmetry and structural alignment between the two substructures. Conversely, a lower score suggests less symmetry and structural similarity.
* GOSim (GO annotation similarity): \(GOSim\) is a similarity metric that is defined to compare the similarity of two biological networks above their biochemical performance. Comparing the GO annotation of two biological networks reflects the difference in biochemical performance between two biological networks, which is defined as follows: \[GOSim(P,Q)=\frac{1}{m}\frac{1}{n}\sum_{i=1}^{m}\sum_{j=1}^{n}GOSemSim(p_{i},q_ {j}),\] (3) where \(m\) denotes the number of molecules contained in the biological network \(P\); \(n\) denotes the number of molecules contained in the biological network \(Q\). \(p_{i}\) denotes the \(i\)-th molecule in the biological network \(P\), and \(q_{j}\) denotes the \(j\)-th molecule in biological network \(Q\). GOSemSim [34] is a tool for measuring the similarity between two biological molecules based on their associated Gene Ontology (GO) terms. It calculates a numerical score that reflects the functional similarity between the molecules by evaluating how closely related their GO annotations are.