The University of Southampton
University of Southampton Institutional Repository

Time-invariant degree growth in preferential attachment network models

Time-invariant degree growth in preferential attachment network models
Time-invariant degree growth in preferential attachment network models
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by the observation that the average degree growth of nodes is time invariant in empirical network data, we study the degree dynamics in the relevant class of network models where preferential attachment is combined with heterogeneous node fitness and aging. We propose an analytical framework based on the time invariance of the studied systems and show that it is self-consistent only for two special network growth forms: the uniform and the exponential network growth. Conversely, the breaking of such time invariance explains the winner-takes-all effect in some model settings, revealing the connection between the Bose-Einstein condensation in the Bianconi-Barabási model and similar gelation in superlinear preferential attachment. Aging is necessary to reproduce realistic node degree growth curves and can prevent the winner-takes-all effect under weak conditions. Our results are verified by extensive numerical simulations.
2470-0045
Sun, Jun
cbc6b83e-3571-4f6a-b77d-51a8a20ac839
Medo, Matus
6b0a04c6-d5fb-4545-8135-b1cb47a18257
Staab, Steffen
bf48d51b-bd11-4d58-8e1c-4e6e03b30c49
Sun, Jun
cbc6b83e-3571-4f6a-b77d-51a8a20ac839
Medo, Matus
6b0a04c6-d5fb-4545-8135-b1cb47a18257
Staab, Steffen
bf48d51b-bd11-4d58-8e1c-4e6e03b30c49

Sun, Jun, Medo, Matus and Staab, Steffen (2020) Time-invariant degree growth in preferential attachment network models. Physical Review E, 101, [022309]. (doi:10.1103/PhysRevE.101.022309).

Record type: Article

Abstract

Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by the observation that the average degree growth of nodes is time invariant in empirical network data, we study the degree dynamics in the relevant class of network models where preferential attachment is combined with heterogeneous node fitness and aging. We propose an analytical framework based on the time invariance of the studied systems and show that it is self-consistent only for two special network growth forms: the uniform and the exponential network growth. Conversely, the breaking of such time invariance explains the winner-takes-all effect in some model settings, revealing the connection between the Bose-Einstein condensation in the Bianconi-Barabási model and similar gelation in superlinear preferential attachment. Aging is necessary to reproduce realistic node degree growth curves and can prevent the winner-takes-all effect under weak conditions. Our results are verified by extensive numerical simulations.

Text
Time-invariant degree growth in preferential attachment - Accepted Manuscript
Download (624kB)

More information

Accepted/In Press date: 21 January 2020
e-pub ahead of print date: 18 February 2020

Identifiers

Local EPrints ID: 437843
URI: http://eprints.soton.ac.uk/id/eprint/437843
ISSN: 2470-0045
PURE UUID: 09e71532-c17e-451d-900f-aea79742f788
ORCID for Steffen Staab: ORCID iD orcid.org/0000-0002-0780-4154

Catalogue record

Date deposited: 20 Feb 2020 17:30
Last modified: 07 Oct 2020 02:07

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×