WSEAS Transactions on Information Science and Applications
Print ISSN: 1790-0832, E-ISSN: 2224-3402
Volume 23, 2026
Insight into Spectral Graph Theory and Spectral Graph Neural Networks
Authors: , , ,
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Abstract: Graph Neural Networks (GNNs) are a class of neural networks specifically designed to process and extract information from graph-structured data by leveraging its inherent topological structure. Among these, Graph Convolutional Networks (GCNs) extend the concept of convolution—initially developed for Convolutional Neural Networks (ConvNets)—to operate on graphs. A specialized subset of GCNs, Spectral Graph Neural Networks (SGNNs), perform convolution in the spectral domain, drawing upon principles from spectral graph theory and Graph Signal Processing (GSP). In this work, we explore SGNNs by surveying key concepts in spectral graph theory and GSP that underpin their design. We also examine how the convolution operation in ConvNets generalizes to GCNs and highlight applications of GCNs along with existing libraries that implement SGNNs.
Keywords:
Spectral Graph Theory, Graph Signal Processing, Graph Laplacian, Graph Fourier Transform, Graph Neural Networks, Spectral Graph Neural Networks
Pages: 102-114
DOI: 10.37394/23209.2026.23.9