Phase transitions for scaling of structural correlations in directed networks

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

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e., models that generate uncorrelated scale-free networks. Most models to date, however, show structural negative dependencies, caused by finite size effects. We analyze the behavior of these structural negative degree-degree dependencies, using rank based correlation measures, in the directed erased configuration model. We obtain expressions for the scaling as a function of the exponents of the distributions. Moreover, we show that this scaling undergoes a phase transition, where one region exhibits scaling related to the natural cutoff of the network while another region has scaling similar to the structural cutoff for uncorrelated networks. By establishing the speed of convergence of these structural dependencies we are able to assess statistical significance of degree-degree dependencies on finite complex networks when compared to networks generated by the directed erased configuration model.
Original languageEnglish
Pages (from-to)11
Number of pages11
JournalPhysical review E: Statistical, nonlinear, and soft matter physics
Volume92
Issue number2
DOIs
Publication statusPublished - 7 Aug 2015

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Directed Network
Phase Transition
Scaling
scaling
Complex Networks
Configuration
Model
Finite Size Effects
cut-off
Statistical Significance
Speed of Convergence
Scale-free Networks
Null
Exponent
configurations
exponents

Keywords

  • MSC-05C80
  • EWI-26405
  • IR-98154
  • METIS-314996
  • MSC-62H20

Cite this

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title = "Phase transitions for scaling of structural correlations in directed networks",
abstract = "Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e., models that generate uncorrelated scale-free networks. Most models to date, however, show structural negative dependencies, caused by finite size effects. We analyze the behavior of these structural negative degree-degree dependencies, using rank based correlation measures, in the directed erased configuration model. We obtain expressions for the scaling as a function of the exponents of the distributions. Moreover, we show that this scaling undergoes a phase transition, where one region exhibits scaling related to the natural cutoff of the network while another region has scaling similar to the structural cutoff for uncorrelated networks. By establishing the speed of convergence of these structural dependencies we are able to assess statistical significance of degree-degree dependencies on finite complex networks when compared to networks generated by the directed erased configuration model.",
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Phase transitions for scaling of structural correlations in directed networks. / van der Hoorn, W.L.F.; Litvak, Nelli.

In: Physical review E: Statistical, nonlinear, and soft matter physics, Vol. 92, No. 2, 07.08.2015, p. 11.

Research output: Contribution to journalArticleAcademicpeer-review

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

AU - Litvak, Nelli

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N2 - Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e., models that generate uncorrelated scale-free networks. Most models to date, however, show structural negative dependencies, caused by finite size effects. We analyze the behavior of these structural negative degree-degree dependencies, using rank based correlation measures, in the directed erased configuration model. We obtain expressions for the scaling as a function of the exponents of the distributions. Moreover, we show that this scaling undergoes a phase transition, where one region exhibits scaling related to the natural cutoff of the network while another region has scaling similar to the structural cutoff for uncorrelated networks. By establishing the speed of convergence of these structural dependencies we are able to assess statistical significance of degree-degree dependencies on finite complex networks when compared to networks generated by the directed erased configuration model.

AB - Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e., models that generate uncorrelated scale-free networks. Most models to date, however, show structural negative dependencies, caused by finite size effects. We analyze the behavior of these structural negative degree-degree dependencies, using rank based correlation measures, in the directed erased configuration model. We obtain expressions for the scaling as a function of the exponents of the distributions. Moreover, we show that this scaling undergoes a phase transition, where one region exhibits scaling related to the natural cutoff of the network while another region has scaling similar to the structural cutoff for uncorrelated networks. By establishing the speed of convergence of these structural dependencies we are able to assess statistical significance of degree-degree dependencies on finite complex networks when compared to networks generated by the directed erased configuration model.

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KW - IR-98154

KW - METIS-314996

KW - MSC-62H20

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JO - Physical review E: covering statistical, nonlinear, biological, and soft matter physics

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