IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v153y2022icp183-197.html
   My bibliography  Save this article

Remarks on power-law random graphs

Author

Listed:
  • Yin, Mei

Abstract

The theory of graphons is an important tool in understanding properties of large networks. We investigate a power-law random graph model and cast it in the graphon framework. The distinctively different structures of the limit graph are explored in detail in the sub-critical and super-critical regimes. In the sub-critical regime, the graph is empty with high probability, and in the rare event that it is non-empty, it consists of a single edge. Contrarily, in the super-critical regime, a non-trivial random graph exists in the limit, and it serves as an uncovered boundary case between different types of graph convergence.

Suggested Citation

  • Yin, Mei, 2022. "Remarks on power-law random graphs," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 183-197.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:183-197
    DOI: 10.1016/j.spa.2022.08.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922001764
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.08.002?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. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    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. Bikramjit Das & Tiandong Wang & Gengling Dai, 2022. "Asymptotic Behavior of Common Connections in Sparse Random Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2071-2092, September.
    2. Pe[combining cedilla]ski, Marcin, 2011. "Prior symmetry, similarity-based reasoning, and endogenous categorization," Journal of Economic Theory, Elsevier, vol. 146(1), pages 111-140, January.
    3. Olav Kallenberg, 1999. "Multivariate Sampling and the Estimation Problem for Exchangeable Arrays," Journal of Theoretical Probability, Springer, vol. 12(3), pages 859-883, July.
    4. Bryan S. Graham & Fengshi Niu & James L. Powell, 2019. "Kernel Density Estimation for Undirected Dyadic Data," Papers 1907.13630, arXiv.org.
    5. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    6. Bryan S. Graham, 2020. "Sparse network asymptotics for logistic regression," Papers 2010.04703, arXiv.org.
    7. Bryan S. Graham, 2019. "Network Data," Papers 1912.06346, arXiv.org.
    8. Harold D Chiang & Yukun Ma & Joel Rodrigue & Yuya Sasaki, 2021. "Dyadic double/debiased machine learning for analyzing determinants of free trade agreements," Papers 2110.04365, arXiv.org, revised Dec 2022.
    9. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.
    10. Olav Kallenberg, 2012. "Schoenberg’s Theorem and Unitarily Invariant Random Arrays," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1013-1039, December.
    11. Eric Auerbach, 2019. "Identification and Estimation of a Partially Linear Regression Model using Network Data," Papers 1903.09679, arXiv.org, revised Jun 2021.
    12. Kameswarrao S. Casukhela, 1997. "Symmetric Distributions of Random Measures in Higher Dimensions," Journal of Theoretical Probability, Springer, vol. 10(3), pages 759-771, July.
    13. Volfovsky, Alexander & Airoldi, Edoardo M., 2016. "Sharp total variation bounds for finitely exchangeable arrays," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 54-59.
    14. Caron, François & Panero, Francesca & Rousseau, Judith, 2023. "On sparsity, power-law, and clustering properties of graphex processes," LSE Research Online Documents on Economics 119794, London School of Economics and Political Science, LSE Library.
    15. Bryan S. Graham, 2019. "Dyadic Regression," Papers 1908.09029, arXiv.org.
    16. Bryan S. Graham, 2019. "Network Data," CeMMAP working papers CWP71/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. DeMuse, Ryan & Yin, Mei, 2021. "Dimension reduction in vertex-weighted exponential random graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    18. Harold D. Chiang & Kengo Kato & Yuya Sasaki, 2023. "Inference for High-Dimensional Exchangeable Arrays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1595-1605, July.
    19. Peter D. Hoff, 2009. "Multiplicative latent factor models for description and prediction of social networks," Computational and Mathematical Organization Theory, Springer, vol. 15(4), pages 261-272, December.
    20. Paolo Leonetti, 2018. "Finite Partially Exchangeable Laws Are Signed Mixtures of Product Laws," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-214, 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:spapps:v:153:y:2022:i:c:p:183-197. 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.