Graph Shift Operator

Graph shift operators are fundamental components of graph neural networks (GNNs), defining how information propagates across graph structures. Current research focuses on improving GNN stability and expressivity by analyzing the properties of these operators, including their spectral characteristics and relationships to graph topology, and exploring variations such as diffusion maps and cross-covariance-based operators within different GNN architectures like EdgeNet and aggregation GNNs. This work aims to enhance GNN performance, particularly in tasks involving noisy or perturbed graphs, and improve our theoretical understanding of GNN capabilities and limitations. The resulting advancements have significant implications for various applications, including time series forecasting, anomaly detection, and signal processing on complex data structures.