Phase transitions for scaling of structural correlations in directed networks

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

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 languageUndefined
Pages (from-to)11
Number of pages11
JournalPhysical review E: Statistical, nonlinear, and soft matter physics
Volume92
Issue number2
DOIs
StatePublished - 7 Aug 2015

Fingerprint

Complex networks
Phase transitions

Keywords

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

Cite this

van der Hoorn, W.L.F.; Litvak, Nelli / Phase transitions for scaling of structural correlations in directed networks.

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

Research output: Scientific - peer-reviewArticle

@article{8f4a063255ba46f6ac376553a7f01b50,
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.",
keywords = "MSC-05C80, EWI-26405, IR-98154, METIS-314996, MSC-62H20",
author = "{van der Hoorn}, W.L.F. and Nelli Litvak",
note = "eemcs-eprint-26405",
year = "2015",
month = "8",
doi = "10.1103/PhysRevE.92.022803",
volume = "92",
pages = "11",
journal = "Physical review E: covering statistical, nonlinear, biological, and soft matter physics",
issn = "2470-0045",
publisher = "American Physical Society",
number = "2",

}

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: Scientific - peer-reviewArticle

TY - JOUR

T1 - Phase transitions for scaling of structural correlations in directed networks

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

AU - Litvak,Nelli

N1 - eemcs-eprint-26405

PY - 2015/8/7

Y1 - 2015/8/7

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.

KW - MSC-05C80

KW - EWI-26405

KW - IR-98154

KW - METIS-314996

KW - MSC-62H20

U2 - 10.1103/PhysRevE.92.022803

DO - 10.1103/PhysRevE.92.022803

M3 - Article

VL - 92

SP - 11

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

T2 - Physical review E: covering statistical, nonlinear, biological, and soft matter physics

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

SN - 2470-0045

IS - 2

ER -