Understanding Spectral Graph Neural Network

Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using algebraic methods to analyze the spectrum of the adjacency matrix or Laplacian matrix of a graph, which lays the foundation of graph convolutional neural networks. This report is more than notes and self-contained which comes from my Ph.D. first-year report literature review part, it illustrates how the graph convolutional neural network model is motivated by spectral graph theory, and discusses the major spectral-based models associated with their fundamentals. The practical applications of the graph convolutional neural networks defined in the spectral domain are also reviewed.