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Clustering time-evolving networks using the spatiotemporal graph Laplacian.

Maia Trower1, Natasa Djurdjevac Conrad2, Stefan Klus3

  • 1Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot-Watt University, EH8 9BT Edinburgh, United Kingdom.

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Summary
This summary is machine-generated.

This study introduces a novel spatiotemporal graph Laplacian for analyzing dynamic graphs. It effectively captures evolving communities in complex systems like social networks and traffic flow.

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Area of Science:

  • Graph theory
  • Dynamical systems
  • Network science

Background:

  • Time-evolving graphs are crucial for modeling dynamic systems like social networks and traffic.
  • Analyzing community structures in these dynamic graphs presents a significant challenge.
  • Existing spectral clustering methods are primarily designed for static graphs.

Purpose of the Study:

  • To generalize spectral clustering algorithms for dynamic graphs.
  • To develop a framework for capturing the temporal evolution of clusters.
  • To introduce and analyze the spectral properties of a spatiotemporal graph Laplacian.

Main Methods:

  • Generalized spectral clustering using canonical correlation analysis.
  • Defined and investigated the spectral properties of the spatiotemporal graph Laplacian.
  • Connected concepts to dynamical systems theory via transfer operators.

Main Results:

  • The proposed method effectively captures temporal cluster evolution.
  • Demonstrated advantages over existing methods on benchmark graphs.
  • The spatiotemporal graph Laplacian provides clear interpretations of cluster dynamics.

Conclusions:

  • The spatiotemporal graph Laplacian is a powerful tool for analyzing time-evolving graph communities.
  • This approach offers a robust method for understanding dynamic network structures.
  • The framework is applicable to both directed and undirected graphs.