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.
Sun, Jun
cbc6b83e-3571-4f6a-b77d-51a8a20ac839
Medo, Matus
6b0a04c6-d5fb-4545-8135-b1cb47a18257
Staab, Steffen
bf48d51b-bd11-4d58-8e1c-4e6e03b30c49
18 February 2020
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 (2), [022309].
(doi:10.1103/PhysRevE.101.022309).
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
More information
Accepted/In Press date: 21 January 2020
e-pub ahead of print date: 18 February 2020
Published date: 18 February 2020
Additional Information:
Funding Information:
We would like to thank the APS for providing us with the citation data. This work is supported by the EU Horizon 2020 project CUTLER ( www.cutler-h2020.eu ) under Contract No. 770469, the Swiss National Science Foundation (Grant No. 200020-156188), and the National Natural Science Foundation of China (Grant No. 11850410444). We appreciate helpful discussions with S. d. Nigris.
Publisher Copyright:
©2020 American Physical Society.
Identifiers
Local EPrints ID: 437843
URI: http://eprints.soton.ac.uk/id/eprint/437843
ISSN: 2470-0045
PURE UUID: 09e71532-c17e-451d-900f-aea79742f788
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Date deposited: 20 Feb 2020 17:30
Last modified: 17 Mar 2024 03:38
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Author:
Jun Sun
Author:
Matus Medo
Author:
Steffen Staab
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