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

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

Research output: Contribution to journalArticleAcademicpeer-review

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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

Cite this

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title = "Convergence of rank based degree-degree correlations in random directed networks",
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.",
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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Convergence of rank based degree-degree correlations in random directed networks. / van der Hoorn, W.L.F.; Litvak, Nelli.

In: Moscow journal of combinatorics and number theory, Vol. 4, No. 4, 2014, p. 45-83.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Convergence of rank based degree-degree correlations in random directed networks

AU - van der Hoorn, W.L.F.

AU - Litvak, Nelli

N1 - eemcs-eprint-26085

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - EWI-26085

KW - AMS-05C80

KW - AMS-62H10

KW - Rank correlations

KW - Kendall’s tau

KW - IR-96226

KW - Degree-degree dependencies

KW - Directed configuration model

KW - Directed random graphs

KW - METIS-312640

KW - Spearman’s rho

M3 - Article

VL - 4

SP - 45

EP - 83

JO - Moscow journal of combinatorics and number theory

JF - Moscow journal of combinatorics and number theory

SN - 2220-5438

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ER -