Unifying Spectral and Spatial Graph Neural Networks

In recent years, Graph Neural Networks (GNNs) have attracted considerable attention. However, the rapid emergence of diverse GNN models, each grounded in different theoretical foundations, complicates the model selection process, as these models are not easily understood within a unified framework. Initial GNNs were constructed using spectral theory, while others were developed based on spatial theory. This theoretical divergence makes direct comparisons difficult. Furthermore, the variety of models within each theoretical domain further complicates their evaluation. In this tutorial, we explore state-of-the-art GNNs and present a comprehensive framework that bridges the spatial and spectral domains, clarifying their interrelationship. This framework deepens our understanding of GNN operations. The tutorial delves into key paradigms, such as spatial and spectral methods, through a synthesis of spectral graph theory and approximation theory. We conduct an in-depth analysis of recent research advancements, addressing emerging issues like over-smoothing, using well-established GNN models to illustrate the universality of our framework.