## 2 Materials and Methods
### The Model of GBNSS  
GBNSS leverages GNNs to learn effective representations of biological networks, integrating both topological and biological features. In particular, GBNSS consists of three main components: feature generation, model training, and similarity query. In the feature generation phase, both topological and biological features are extracted from each node in the biological networks. The model training phase employs a GNN architecture comprising multiple graph convolution layers and a graph attention layer, which is trained to predict the similarity scores between pairs of biological networks. Finally, in the similarity query phase, the trained model is utilized to compute the similarity scores between a query network and a database of biological networks, facilitating efficient and accurate similarity searches. Figure 3 visualizes the scheme of GBNSS. The GBNSS framework encompasses three pivotal stages--feature generation, model training, and similarity query--with each contributing to the overarching goal of facilitating efficient and accurate similarity searches among biological networks. * Feature Generation Stage: At the feature generation stage, both topological and biochemical features are extracted from the biological networks. Topological features, inspired by the bag-of-words model, capture the presence or absence of nodes across a set of biological networks. Meanwhile, biochemical features are derived from Gene Ontology annotations, categorizing nodes based on molecular function, cellular component, and biological process. Together, these features provide comprehensive representations of the structural and functional characteristics of nodes in biological networks. * Model Training Stage: The model training stage harnesses the power of graph neural networks (GNNs) to learn effective representations of biological networks. GBNSS employs a GNN architecture comprising multiple graph convolutional layers and a graph attention layer. During training, the model is optimized to predict similarity scores between pairs of biological networks, using metrics EC, LCCS, and S3 for topological similarity and GOSim for biochemical similarity. By minimizing the mean squared error (MSE) loss, the model learns to capture intricate relationships and nuances within and between biological networks. Specifically, when predicting the topological similarity between two networks, we use topological features as input because they directly capture the structural aspects relevant to the task. Similarly, for biochemical feature similarity prediction, using biological features as input aligns  
Figure 3: The scheme of GBNSS. The dotted line in Step 1 indicates the data preprocessing, the dotted line in Step 2 indicates the model training, and the solid line in Step 3 indicates the querying. better with the nature of the target. The pseudo-code of GBNSS's model training is presented in Algorithm 1. * Similarity Query Stage: In the final stage, the trained model is deployed for similarity query tasks. Given a query biological network and a database biological network, the model GBNSS computes their similarity score. These scores are then used to rank the database networks in descending order of similarity, yielding the final similarity query results. By leveraging the model's learned representations and predictive capabilities, GBNSS enables efficient and accurate identification of biologically relevant network relationships. Four distinct models are provided after model training. Three models focus on topological similarity, using EC, LCCS, and S3 as labels, while the fourth model targets biochemical similarity with GOSim as the label. During inference, users can choose the model that best suits their specific needs and provide the relevant input data accordingly.