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Modeling graphs using dot product representations

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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).

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References

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, 21218, USA

    Edward R. Scheinerman

  2. Department of Mathematics, Harvey Mudd College, Claremont, CA, 91711, USA

    Kimberly Tucker

Authors
  1. Edward R. Scheinerman
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  2. Kimberly Tucker
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Correspondence to Edward R. Scheinerman.

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Scheinerman, E.R., Tucker, K. Modeling graphs using dot product representations. Comput Stat 25, 1–16 (2010). https://doi.org/10.1007/s00180-009-0158-8

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  • DOI: https://doi.org/10.1007/s00180-009-0158-8

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