Reciprocity of networks with degree correlations and arbitrary degree sequences

Gorka Zamora-Lopez, Vinko Zlatic, Changsong Zhou, Hrvoje Stefancic, Juergen Kurths

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity r has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with arbitrary input and output degree sequences and given 2-node degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to r is revealed. Numerical experiments using network randomization methods show very good agreement to our analytical estimations.

Original languageEnglish
Article number016106
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume77
Issue number1
DOIs
Publication statusPublished - 16 Jan 2008

Cite this

Reciprocity of networks with degree correlations and arbitrary degree sequences. / Zamora-Lopez, Gorka; Zlatic, Vinko; Zhou, Changsong; Stefancic, Hrvoje; Kurths, Juergen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 77, No. 1, 016106, 16.01.2008.

Research output: Contribution to journalArticle

Zamora-Lopez, Gorka ; Zlatic, Vinko ; Zhou, Changsong ; Stefancic, Hrvoje ; Kurths, Juergen. / Reciprocity of networks with degree correlations and arbitrary degree sequences. In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics. 2008 ; Vol. 77, No. 1.
@article{b7c289567d214afab268c8944c3b4d60,
title = "Reciprocity of networks with degree correlations and arbitrary degree sequences",
abstract = "Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity r has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with arbitrary input and output degree sequences and given 2-node degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to r is revealed. Numerical experiments using network randomization methods show very good agreement to our analytical estimations.",
author = "Gorka Zamora-Lopez and Vinko Zlatic and Changsong Zhou and Hrvoje Stefancic and Juergen Kurths",
year = "2008",
month = "1",
day = "16",
doi = "10.1103/PhysRevE.77.016106",
language = "English",
volume = "77",
journal = "Physical Review. E, Statistical, Nonlinear and Soft Matter Physics",
issn = "1539-3755",
publisher = "AMER PHYSICAL SOC",
number = "1",

}

TY - JOUR

T1 - Reciprocity of networks with degree correlations and arbitrary degree sequences

AU - Zamora-Lopez, Gorka

AU - Zlatic, Vinko

AU - Zhou, Changsong

AU - Stefancic, Hrvoje

AU - Kurths, Juergen

PY - 2008/1/16

Y1 - 2008/1/16

N2 - Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity r has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with arbitrary input and output degree sequences and given 2-node degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to r is revealed. Numerical experiments using network randomization methods show very good agreement to our analytical estimations.

AB - Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity r has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with arbitrary input and output degree sequences and given 2-node degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to r is revealed. Numerical experiments using network randomization methods show very good agreement to our analytical estimations.

U2 - 10.1103/PhysRevE.77.016106

DO - 10.1103/PhysRevE.77.016106

M3 - Article

VL - 77

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 1

M1 - 016106

ER -