N2GON: Neural Networks for Graph-of-Net with Position Awareness

Graphs, fundamental in modeling various research subjects such as computing networks, consist of nodes linked by edges. However, they typically function as components within larger structures in real-world scenarios, such as in proteinprotein interactions where each protein is a graph in a larger network. This study delves into the Graph-of-Net (GON), a structure that extends the concept of traditional graphs by representing each node as a graph itself. It provides a multi-level perspective on the relationships between objects, encapsulating both the detailed structure of individual nodes and the broader network of dependencies. To learn node representations within the GON, we propose a position-aware neural network for Graph-of-Net which processes both intragraph and inter-graph connections and incorporates additional data like node labels. Our model employs dual encoders and graph constructors to build and refine a constraint network, where nodes are adaptively arranged based on their positions, as determined by the network's constraint system. Our model demonstrates significant improvements over baselines in empirical evaluations on various datasets.