IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v561y2021ics0378437120306804.html
   My bibliography  Save this article

Dimension reduction in vertex-weighted exponential random graphs

Author

Listed:
  • DeMuse, Ryan
  • Yin, Mei

Abstract

We investigate the behavior of vertex-weighted exponential random graphs. We show that vertex-weighted exponential random graphs with edge weights induced by products of independent vertex weights are approximate mixtures of graphs whose vertex weight vector is a near fixed point of a certain vector equation. For graphs with Hamiltonians counting cliques, it is demonstrated that, under appropriate conditions, every solution to this equation is close to a block vector with a small number of communities. We prove that for the cases of positive weights and small weights in the Hamiltonian in particular, the vector equation has a unique solution. Lastly, the behavior of vertex-weighted exponential random graphs counting triangles is studied in detail and the solution to the vector equation is shown to approach the zero vector as the weight diverges to negative infinity for sufficiently large networks.

Suggested Citation

  • DeMuse, Ryan & Yin, Mei, 2021. "Dimension reduction in vertex-weighted exponential random graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    • Handle: RePEc:eee:phsmap:v:561:y:2021:i:c:s0378437120306804
    DOI: 10.1016/j.physa.2020.125289
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120306804
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.125289?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. Cranmer, Skyler J. & Desmarais, Bruce A., 2011. "Inferential Network Analysis with Exponential Random Graph Models," Political Analysis, Cambridge University Press, vol. 19(1), pages 66-86, January.
    2. 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. Darko Cherepnalkoski & Andreas Karpf & Igor Mozetič & Miha Grčar, 2016. "Cohesion and Coalition Formation in the European Parliament: Roll-Call Votes and Twitter Activities," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-27, November.
    2. Jochmans, Koen, 2024. "Nonparametric identification and estimation of stochastic block models from many small networks," Journal of Econometrics, Elsevier, vol. 242(2).
    3. 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.
    4. Cornelius Fritz & Michael Lebacher & Göran Kauermann, 2020. "Tempus volat, hora fugit: A survey of tie‐oriented dynamic network models in discrete and continuous time," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 275-299, August.
    5. Ruslan Rinatovich Abezgildin, 0. "Relevant Issues Determining the Effectiveness of Policy Networks," Administrative Consulting, Russian Presidential Academy of National Economy and Public Administration. North-West Institute of Management., issue 10.
    6. Olav Kallenberg, 1999. "Multivariate Sampling and the Estimation Problem for Exchangeable Arrays," Journal of Theoretical Probability, Springer, vol. 12(3), pages 859-883, July.
    7. Olivier Godechot & Joanne Horton & Yuval Millo, 2022. "Executive Pay: Board Reciprocity Counts," Post-Print hal-03924965, HAL.
    8. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    9. Jan Beyers & Tom Donas, 2014. "Inter-regional networks in Brussels: Analyzing the information exchanges among regional offices," European Union Politics, , vol. 15(4), pages 547-571, December.
    10. Bryan S. Graham, 2020. "Sparse network asymptotics for logistic regression," Papers 2010.04703, arXiv.org.
    11. Bryan S. Graham, 2019. "Network Data," Papers 1912.06346, arXiv.org.
    12. 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.
    13. Dong, Qingli & Zhao, Yanzhi & Ma, Xiaojun & Zhou, Yanan, 2024. "Risk spillover between carbon markets and stock markets from a progressive perspective: Measurements, spillover networks, and driving factors," Energy Economics, Elsevier, vol. 129(C).
    14. Kameswarrao S. Casukhela, 1997. "Symmetric Distributions of Random Measures in Higher Dimensions," Journal of Theoretical Probability, Springer, vol. 10(3), pages 759-771, July.
    15. Bryan S. Graham & Fengshi Niu & James L. Powell, 2019. "Kernel density estimation for undirected dyadic data," CeMMAP working papers CWP39/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Bryan S. Graham, 2019. "Dyadic Regression," Papers 1908.09029, arXiv.org.
    17. Graham, Bryan S. & Niu, Fengshi & Powell, James L., 2024. "Kernel density estimation for undirected dyadic data," Journal of Econometrics, Elsevier, vol. 240(2).
    18. Scott W. Duxbury, 2024. "Collaborating on the Carceral State: Political Elite Polarization and the Expansion of Federal Crime Legislation Networks, 1979 to 2005," American Sociological Review, , vol. 89(4), pages 650-683, August.
    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. Bryan S. Graham, 2024. "Sparse Network Asymptotics for Logistic Regression Under Possible Misspecification," Econometrica, Econometric Society, vol. 92(6), pages 1837-1868, November.

    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:phsmap:v:561:y:2021:i:c:s0378437120306804. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.