Abstract: Graph neural networks are powerful models for learning graph-structured data,representing them through node information embedding and graph convolution operations.In graph data,the structural information and positional information of nodes are crucial for extracting graph features.However,existing GNNs have limited expressive ability in simultaneously capturing positional and structural information.This paper proposes a novel graph neural network,named Positional and Structural Information with Graph Neural Networks(PSI-GNN).The core idea of PSI-GNN lies in utilizing an encoder to capture the positional and structural information of nodes and embedding these information features into the network.By updating and propagating these two types of information within the network,PSI-GNN effectively integrates and utilizes positional and structural information,providing an effective solution to the aforementioned problem.Additionally,to accommodate different types of graph learning tasks,PSI-GNN assigns varying weights to positional and structural information based on the specific downstream tasks.To validate the effectiveness of PSI-GNN,experiments are conducted on multiple benchmark graph datasets.The experimental results demonstrate that PSI-GNN achieves a maximum improvement of approximately 14% on node-level tasks and approximately 35% on graph-level tasks.These results confirm the effectiveness of PSI-GNN in simultaneously capturing positional and structural information.

Key words: Graph neural networks, Positional information, Structural information, Laplace position encoding, Adamic-Adar structural encoding