Degree-degree dependencies in directed networks with heavy-tailed degrees

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

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)
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Abstract

In network theory, Pearson’s correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree sequences. We prove that for graphs where the in- and out-degree sequences satisfy a power law with realistic parameters, Pearson’s correlation coefficients converge to a nonnegative number in the infinite network size limit. We propose alternative measures for degree-degree dependencies in directed networks based on Spearman’s rho and Kendall’s tau. Using examples and calculations on the Wikipedia graphs for nine different languages, we show why these rank correlation measures are more suited for measuring degree assortativity in directed graphs with heavy-tailed degrees.
Original languageEnglish
Pages (from-to)155-179
Number of pages25
JournalInternet mathematics
Volume11
Issue number2
DOIs
Publication statusPublished - 2015

Fingerprint

Directed Network
Directed graphs
Circuit theory
Pearson Correlation
Degree Sequence
Correlation coefficient
Spearman's rho
Kendall's tau
Spearman's coefficient
Wikipedia
Graph in graph theory
Directed Graph
Power Law
Non-negative
Converge
Alternatives
Coefficient

Keywords

  • EWI-25536
  • IR-95514
  • METIS-312470

Cite this

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Degree-degree dependencies in directed networks with heavy-tailed degrees. / van der Hoorn, W.L.F.; Litvak, Nelly.

In: Internet mathematics, Vol. 11, No. 2, 2015, p. 155-179.

Research output: Contribution to journalArticleAcademicpeer-review

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