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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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Published on: March 18, 2019

Graph characterization via Ihara coefficients.

Peng Ren1, Richard C Wilson, Edwin R Hancock

  • 1Department of Computer Science, Universityof York, York Y01 5GH, UK. pengren@cs.york.ac.uk

IEEE Transactions on Neural Networks
|December 2, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces Ihara coefficients for graph characterization, offering a permutation-invariant method for unweighted graphs and generalizing it to weighted graphs. These coefficients effectively capture graph structure and outperform Laplacian spectra methods.

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Area of Science:

  • Graph theory
  • Network analysis
  • Spectral methods

Background:

  • Graph characterization is crucial for understanding network structures.
  • Existing methods often lack permutation invariance or struggle with weighted graphs.
  • Ihara zeta function provides insights into graph properties.

Purpose of the Study:

  • To develop a permutation-invariant method for characterizing unweighted graphs using Ihara coefficients.
  • To generalize Ihara coefficients to edge-weighted graphs.
  • To evaluate the effectiveness of Ihara coefficients compared to existing graph spectral methods.

Main Methods:

  • Utilizing polynomial coefficients of the Ihara zeta function for unweighted graphs.
  • Generalizing Ihara coefficients using the reduced Bartholdi zeta function for edge-weighted graphs.
  • Performing spectral analysis of Ihara coefficients and comparing with Laplacian spectra.

Main Results:

  • Ihara coefficients provide a permutation-invariant characterization of unweighted graphs.
  • The method is successfully generalized to edge-weighted graphs.
  • Ihara coefficients demonstrate superior performance in graph-class structure capture and graph clustering compared to Laplacian spectra.

Conclusions:

  • Ihara coefficients offer a robust and effective method for graph characterization.
  • The generalized approach handles both unweighted and edge-weighted graphs.
  • This method presents a significant advancement over traditional spectral graph analysis techniques.