  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.
