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Graph comparison via the nonbacktracking spectrum.

Andrew Mellor1, Angelica Grusovin1

  • 1Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom.

Physical Review. E
|June 20, 2019
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Summary
This summary is machine-generated.

We introduce a novel graph comparison method using the nonbacktracking spectral embedding. This approach reliably compares graphs of varying sizes and mechanisms, overcoming limitations of existing techniques.

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Area of Science:

  • Graph theory
  • Network analysis
  • Data mining

Background:

  • Graph comparison is crucial in diverse fields like biological and social networks.
  • Existing graph distance methods are often not metrics or are computationally infeasible for large graphs.

Purpose of the Study:

  • To define a new, computationally feasible pseudometric for graph comparison.
  • To demonstrate the utility of this pseudometric for comparing graphs of varying sizes and origins.

Main Methods:

  • Utilizing the spectrum of the nonbacktracking graph operator.
  • Developing a nonbacktracking spectral embedding for graphs.
  • Applying the new pseudometric to classify empirical graphs.

Main Results:

  • The proposed pseudometric effectively compares graphs generated by different mechanisms.
  • The method reliably compares graphs of varying sizes.
  • Watts-Strogatz graphs form a manifold in the nonbacktracking spectral embedding.

Conclusions:

  • The nonbacktracking spectral pseudometric offers a robust solution for graph comparison.
  • This method enhances standard data-mining techniques for network analysis.
  • The approach is applicable to real-world graph classification problems.