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An efficient approach of graph isomorphism identification using loop theory and hopfield neural networks

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Abstract

Isomorphism identification of kinematic chains or topological graphs is a crucial issue in structural synthesis and innovative mechanism design. In this paper, a new method of isomorphism identification is proposed based on loop theory and hopfield neural networks. A program is written in Python to execute the method. First, the combination of maximum loops in a graph is generated by graph depth-first traversal algorithm. Then, the maximum loop is determined by its link degree sequence, and the maximum-loop matrix is also ensured by the selected maximum loop. Based on the iteration processes in hopfield neural networks, the maximum-loop matrix is changed from original low-ranking matrix to high-ranking matrix. Finally, some kinematic chains and topological graphs are introduced to justify the effectiveness of the proposed method. Results show that the proposed method applies to isomorphism identification of kinematic chains and topological graphs. And the proposed method is efficient and accurate. It enriches the application of loop theory and neural network for isomorphism identification.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Funding

This work was supported by the Innovation Ability Improvement Project of Science and Technology Small and Medium Enterprises in Shandong Province (Grant no. 2022TSGC2557); Research Project of Education Department of Zhejiang Province (Grant no. Y202248907); Basic Scientific Research Project of Wenzhou City (Grant no. G20220004) and Graduate Scientific Research Foundation of Wenzhou University (Grant no. 3162023003057).

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325035, People’s Republic of China

    Hongbin Wang, An Long, Luchuan Yu & Hongming Zhou

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  1. Hongbin Wang
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  2. An Long
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  3. Luchuan Yu
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  4. Hongming Zhou
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Correspondence to Luchuan Yu or Hongming Zhou.

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Wang, H., Long, A., Yu, L. et al. An efficient approach of graph isomorphism identification using loop theory and hopfield neural networks. Multimed Tools Appl 83, 22545–22566 (2024). https://doi.org/10.1007/s11042-023-16410-w

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  • DOI: https://doi.org/10.1007/s11042-023-16410-w

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