Time-invariant degree growth in preferential attachment network models

• URL: http://arxiv.org/abs/2001.08132v1
• Date: Wed, 22 Jan 2020 16:31:11 GMT
• Title: Time-invariant degree growth in preferential attachment network models
• Authors: Jun Sun, Mat\'u\v{s} Medo, Steffen Staab
• Abstract summary: We study the degree dynamics in a class of network models where preferential attachment is combined with node fitness and aging. We show that it is self-consistent only for two special network growth forms: the uniform and exponential network growth.
• Score: 8.929656934088989
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 a novel 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 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-Barab\'{a}si 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.

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