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Estimating network dimension when the spectrum struggles.

Peter Grindrod1, Desmond J Higham2, Henry-Louis de Kergorlay2

  • 1Mathematical Institute, University of Oxford, OX2 6GG, UK.

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Summary
This summary is machine-generated.

This study introduces a novel method for estimating network dimension by analyzing nearest neighbor distances. This approach offers advantages over traditional spectral embedding techniques for understanding network structure.

Keywords:
box countingeigenvectorgraphnearest neighbourspectral embedding

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Area of Science:

  • Network science
  • Data analysis
  • Dimensionality reduction

Background:

  • Understanding the intrinsic dimensionality of networks is crucial for analyzing complex systems.
  • Existing methods for estimating network dimension often rely on spectral analysis, which can be computationally intensive or visually subjective.

Purpose of the Study:

  • To develop an efficient and accurate method for estimating the dimension of networks.
  • To provide an alternative to spectral gap analysis for network dimension characterization.

Main Methods:

  • Adapting an efficient algorithm for data clouds based on nearest neighbor distances for weighted networks.
  • Extending the algorithm to unweighted networks using spectral embedding.

Main Results:

  • The proposed method effectively estimates network dimension for both weighted and unweighted networks.
  • Demonstrated advantages over traditional spectral analysis, particularly in terms of efficiency and objectivity.

Conclusions:

  • Nearest neighbor distance-based algorithms provide a robust and efficient approach to network dimension estimation.
  • This technique offers a valuable tool for network analysis and understanding complex system structures.