On the graph Laplacian and the rankability of data

Recently, Anderson et al. (2019) proposed the concept of rankability, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. In the same paper, they proposed a rankability measure that is based on an integer program for computing the minimum number of edge changes made to a directed graph in order to obtain a complete dominance graph, i.e., an acyclic tournament graph. In this article, we prove a spectral-degree characterization of complete dominance graphs and apply this characterization to produce a new measure of rankability that is cost-effective and more widely applicable. We support the details of our algorithm with several results regarding the conditioning of the Laplacian spectrum of complete dominance graphs and the Hausdorff distance between their Laplacian spectrum and that of an arbitrary directed graph with weights between zero and one. Finally, we analyze the rankability of datasets from the world of chess and college football.

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Work Title On the graph Laplacian and the rankability of data
Open Access
  1. Thomas R. Cameron
  2. Amy N. Langville
  3. Heather C. Smith
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
  1. Elsevier BV
Publication Date March 2020
Publisher Identifier (DOI)
  1. 10.1016/j.laa.2019.11.026
  1. Linear Algebra and its Applications
Deposited September 09, 2021




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  • Added Creator Thomas R. Cameron
  • Added Creator Amy N. Langville
  • Added Creator Heather C. Smith
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