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Mathematics > Probability

arXiv:1407.7662 (math)
[Submitted on 29 Jul 2014 (v1), last revised 30 Oct 2014 (this version, v3)]

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

Authors:Pim van der Hoorn, Nelly 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.
Subjects: Probability (math.PR)
MSC classes: 62H20, 05C80
Cite as: arXiv:1407.7662 [math.PR]
  (or arXiv:1407.7662v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1407.7662

Submission history

From: Pim van der Hoorn [view email]
[v1] Tue, 29 Jul 2014 08:24:53 UTC (24 KB)
[v2] Tue, 14 Oct 2014 14:23:46 UTC (23 KB)
[v3] Thu, 30 Oct 2014 13:04:04 UTC (23 KB)
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