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Related Experiment Video

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Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Published on: October 28, 2018

Graph isomorphisms and automorphisms via spectral signatures.

Dan Raviv¹, Ron Kimmel, Alfred M Bruckstein

¹Department of Computer Science, Technion-Israel Institute of Technology, Taub Building, Haifa 32000, Israel. darav@cs.technion.ac.il

IEEE Transactions on Pattern Analysis and Machine Intelligence

|June 22, 2013

Summary

We present an efficient graph isomorphism algorithm using heat kernels. This method offers practical polynomial runtime for finding graph structures and their symmetries.

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Area of Science:

Graph theory
Computational mathematics
Network analysis

Background:

Graph isomorphism is crucial for applied sciences, yet its computational complexity remains an open problem.
Existing methods often struggle with large or complex graph structures.

Purpose of the Study:

To introduce an efficient computational method for determining graph isomorphisms and automorphisms.
To demonstrate the practical applicability and performance of the proposed technique.

Main Methods:

Utilizing heat kernels derived from the graph Laplacian.
Developing a novel algorithm for computing graph mappings.

Main Results:

The method achieves practical polynomial runtime in the number of vertices.
The algorithm successfully handles diverse graph types and sizes.
Performance is competitive with current state-of-the-art graph isomorphism packages.

Conclusions:

The heat kernel approach provides an efficient solution for graph isomorphism and automorphism detection.
This method offers a practical alternative for analyzing complex graph structures in various scientific domains.