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Modeling graphs using dot product representations

Author

Listed:
  • Edward R. Scheinerman

    (Johns Hopkins University)

  • Kimberly Tucker

    (Harvey Mudd College)

Abstract

Given a simple (weighted) graph, or a collection of graphs on a common vertex set, we seek an assignment of vectors to the vertices such that the dot products of these vectors approximate the weight/frequency of the edges. By transforming vertices into (low dimensional) vectors, one can bring geometric methods to bear in the analysis of the graph(s). We illustrate our approach on the Mathematicians Collaboration Graph [Grossman (1996) The Erdős number project, http://www.oakland.edu/enp ] and the times series of Interstate Alliance Graphs (Gibler and Sarkees in J Peace Res 41(2):211–222, 2004).

Suggested Citation

  • Edward R. Scheinerman & Kimberly Tucker, 2010. "Modeling graphs using dot product representations," Computational Statistics, Springer, vol. 25(1), pages 1-16, March.
    • Handle: RePEc:spr:compst:v:25:y:2010:i:1:d:10.1007_s00180-009-0158-8
    DOI: 10.1007/s00180-009-0158-8
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    References listed on IDEAS

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    1. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
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    Cited by:

    1. Chung, Jaewon & Bridgeford, Eric & Arroyo, Jesus & Pedigo, Benjamin D. & Saad-Eldin, Ali & Gopalakrishnan, Vivek & Xiang, Liang & Priebe, Carey E. & Vogelstein, Joshua T., 2020. "Statistical Connectomics," OSF Preprints ek4n3, Center for Open Science.
    2. N. Lee & C. Priebe, 2011. "A latent process model for time series of attributed random graphs," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 231-253, October.

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