IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v358y2019icp1-15.html
   My bibliography  Save this article

Comparing large-scale graphs based on quantum probability theory

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319302693
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.03.061?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Discussion Paper 2007-33, Tilburg University, Center for Economic Research.
    2. Abiad, A. & Haemers, W.H., 2012. "Cospectral Graphs and Regular Orthogonal Matrices of Level 2," Other publications TiSEM c656ae2c-dc83-44be-906c-b, Tilburg University, School of Economics and Management.
    3. Abiad, A. & Haemers, W.H., 2012. "Cospectral Graphs and Regular Orthogonal Matrices of Level 2," Discussion Paper 2012-042, Tilburg University, Center for Economic Research.
    4. Ghorbani, Modjtaba & Dehmer, Matthias & Rajabi-Parsa, Mina & Emmert-Streib, Frank & Mowshowitz, Abbe, 2019. "Hosoya entropy of fullerene graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 88-98.
    5. Yu, Guihai & Li, Xingfu, 2020. "Connective Steiner 3-eccentricity index and network similarity measure," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    6. Aouchiche, Mustapha & Hansen, Pierre, 2018. "Cospectrality of graphs with respect to distance matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 309-321.
    7. Modjtaba Ghorbani & Matthias Dehmer & Frank Emmert-Streib, 2020. "Properties of Entropy-Based Topological Measures of Fullerenes," Mathematics, MDPI, vol. 8(5), pages 1-23, May.
    8. Ilić, Aleksandar & Ilić, Milovan, 2017. "Counterexamples to conjectures on graph distance measures based on topological indexes," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 148-152.
    9. Ghorbani, Modjtaba & Hakimi-Nezhaad, Mardjan & Dehmer, Matthias, 2022. "Novel results on partial hosoya polynomials: An application in chemistry," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    10. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Other publications TiSEM 3827c785-7b51-4bcd-aea3-f, Tilburg University, School of Economics and Management.
    11. Das, Kinkar Ch. & Gutman, Ivan & Nadjafi–Arani, Mohammad J., 2015. "Relations between distance–based and degree–based topological indices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 142-147.
    12. Maryam Jalali-Rad & Modjtaba Ghorbani & Matthias Dehmer & Frank Emmert-Streib, 2021. "Orbit Entropy and Symmetry Index Revisited," Mathematics, MDPI, vol. 9(10), pages 1-13, May.
    13. Liu, Muhuo & Das, Kinkar Ch., 2018. "On the ordering of distance-based invariants of graphs," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 191-201.
    14. Ghorbani, Modjtaba & Dehmer, Matthias & Zangi, Samaneh, 2018. "Graph operations based on using distance-based graph entropies," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 547-555.
    15. Saeree Wananiyakul & Jörn Steuding & Janyarak Tongsomporn, 2022. "How to Distinguish Cospectral Graphs," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    16. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    17. Tianyi Bu & Lizhu Sun & Wenzhe Wang & Jiang Zhou, 2014. "Main Q-eigenvalues and generalized Q-cospectrality of graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(4), pages 531-538, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:1-15. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.