IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v120y2025i550p948-962.html
   My bibliography  Save this article

Optimal Network Membership Estimation under Severe Degree Heterogeneity

Author

Listed:
  • Zheng Tracy Ke
  • Jingming Wang

Abstract

Real networks often have severe degree heterogeneity, with maximum, average, and minimum node degrees differing significantly. This article examines the impact of degree heterogeneity on statistical limits of network data analysis. Introducing the heterogeneity distribution (HD) under a degree-corrected mixed membership model, we show that the optimal rate of mixed membership estimation is an explicit functional of the HD. This result confirms that severe degree heterogeneity decelerates the error rate, even when the overall sparsity remains unchanged. To obtain a rate-optimal method, we modify an existing spectral algorithm, Mixed-SCORE, by adding a pre-PCA normalization step. This step normalizes the adjacency matrix by a diagonal matrix consisting of the bth power of node degrees, for some b∈R . We discover that b = 1/2 is universally favorable. The resulting spectral algorithm is rate-optimal for networks with arbitrary degree heterogeneity. A technical component in our proofs is entry-wise eigenvector analysis of the normalized graph Laplacian. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Suggested Citation

  • Zheng Tracy Ke & Jingming Wang, 2025. "Optimal Network Membership Estimation under Severe Degree Heterogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 120(550), pages 948-962, April.
  • Handle: RePEc:taf:jnlasa:v:120:y:2025:i:550:p:948-962
    DOI: 10.1080/01621459.2024.2388903
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2024.2388903
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2024.2388903?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.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlasa:v:120:y:2025:i:550:p:948-962. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.