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Comparing large-scale graphs based on quantum probability theory

Author

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  • Choi, Hayoung
  • Lee, Hosoo
  • Shen, Yifei
  • Shi, Yuanming

Abstract

In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our proposed distance between two graphs is defined as the distance between the corresponding moment matrices of their spectral distributions. It is shown that the spectral distributions of their adjacency matrices in a vector state includes information not only about their eigenvalues, but also about the corresponding eigenvectors. Moreover, we prove that the proposed distance is graph invariant and sub-structure invariant. Examples with various graphs are given, and distances between graphs with few vertices are checked. Computational results for real large-scale graphs show that its accuracy is better than any existing methods and time cost is extensively cheap.

Suggested Citation

  • Choi, Hayoung & Lee, Hosoo & Shen, Yifei & Shi, Yuanming, 2019. "Comparing large-scale graphs based on quantum probability theory," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 1-15.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:1-15
    DOI: 10.1016/j.amc.2019.03.061
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H. & Koolen, J.H., 2006. "Cospectral Graphs and the Generalized Adjacency Matrix," Discussion Paper 2006-31, Tilburg University, Center for Economic Research.
    2. Dehmer, Matthias & Emmert-Streib, Frank & Shi, Yongtang, 2015. "Graph distance measures based on topological indices revisited," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 623-633.
    3. Dehmer, Matthias & Varmuza, Kurt, 2015. "A comparative analysis of the Tanimoto index and graph edit distance for measuring the topological similarity of trees," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 242-250.
    Full references (including those not matched with items on IDEAS)

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