Convergence of rank based degree-degree correlations in random directed networks

W.L.F. van der Hoorn, Nelli Litvak

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Abstract

We introduce, and analyze, three measures for degree-degree dependencies, also called degree assortativity, in directed random graphs, based on Spearman’s rho and Kendall’s tau. We proof statistical consistency of these measures in general random graphs and show that the directed Configuration Model can serve as a null model for our degree-degree dependency measures. Based on these results we argue that the measures we introduce should be preferred over Pearson’s correlation coefficients, when studying degree-degree dependencies, since the latter has several issues in the case of large networks with scale-free degree distributions.
Original languageUndefined
Pages (from-to)45-83
Number of pages39
JournalMoscow journal of combinatorics and number theory
Volume4
Issue number4
Publication statusPublished - 2014

Keywords

  • EWI-26085
  • AMS-05C80
  • AMS-62H10
  • Rank correlations
  • Kendall’s tau
  • IR-96226
  • Degree-degree dependencies
  • Directed configuration model
  • Directed random graphs
  • METIS-312640
  • Spearman’s rho

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