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A spectral graph convolution for signed directed graphs via magnetic Laplacian.

Taewook Ko1, Yoonhyuk Choi1, Chong-Kwon Kim2

  • 1Seoul National University, Seoul, Republic of Korea.

Neural Networks : the Official Journal of the International Neural Network Society
|May 22, 2023
PubMed
Summary

This study introduces a new spectral graph convolution model for analyzing complex signed directed graphs. The novel magnetic Laplacian matrix effectively captures edge information, outperforming existing methods for graph embedding.

Keywords:
Graph convolutionLink existence predictionLink sign predictionMagnetic LaplacianSigned directed graphsSpectral convolution

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Area of Science:

  • Graph Theory
  • Machine Learning
  • Data Science

Background:

  • Signed directed graphs offer richer information than simpler graph types.
  • Analyzing these complex graphs is challenging due to limited methods.
  • Existing research has not fully explored the potential of signed directed graphs.

Purpose of the Study:

  • To propose a novel spectral graph convolution model for signed directed graphs.
  • To develop a method that effectively captures underlying patterns and edge information.
  • To improve graph embedding techniques for signed directed graphs.

Main Methods:

  • Introduction of a complex Hermitian adjacency matrix to represent edge sign and direction.
  • Definition of a magnetic Laplacian matrix for spectral convolution.
  • Demonstration of the positive semi-definite (PSD) property of the magnetic Laplacian matrix.

Main Results:

  • The magnetic Laplacian matrix captures additional edge information compared to traditional Laplacians.
  • The proposed model generates more representative embeddings by leveraging signed directed edge information.
  • The method shows wide applicability across various graph types and represents a generalized Laplacian form.

Conclusions:

  • The novel spectral graph convolution model effectively analyzes signed directed graphs.
  • The magnetic Laplacian matrix is a powerful tool for capturing complex graph structures.
  • The proposed method achieves state-of-the-art performance in signed directed graph embedding.