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Random processes with high variance produce scale free networks.

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Title: Random processes with high variance produce scale free networks.
Authors: Johnston, Josh1 (AUTHOR) jjohnston@u.boisestate.edu, Andersen, Tim1 (AUTHOR) tandersen@boisestate.edu
Source: Physica A. Oct2022, Vol. 604, pN.PAG-N.PAG. 1p.
Subjects: Central limit theorem, Geometric distribution, Random graphs
Abstract: Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms leading to these networks and are incorporated in the Barabási–Albert (BA) model (Barabási, 2009 [1]). We provide an alternative model using a randomly stopped linking process inspired by a generalized Central Limit Theorem (CLT) for geometric distributions with widely varying parameters. The common characteristic of both the BA model and our randomly stopped linking model is the mixture of widely varying geometric distributions, suggesting the critical characteristic of scale free networks is high variance, not growth or preferential attachment. The limitation of classical random graph models is low variance in parameters, while scale free networks are the natural, expected result of real-world variance. • Randomly stopped linking model generates scale free networks. • Scale free networks expected from any Bernoulli process with high variance. • Preferential attachment and growth not needed for scale free networks. • Heavy-tailed degree distributions come from mixture of geometric distributions. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms leading to these networks and are incorporated in the Barabási–Albert (BA) model (Barabási, 2009 [1]). We provide an alternative model using a randomly stopped linking process inspired by a generalized Central Limit Theorem (CLT) for geometric distributions with widely varying parameters. The common characteristic of both the BA model and our randomly stopped linking model is the mixture of widely varying geometric distributions, suggesting the critical characteristic of scale free networks is high variance, not growth or preferential attachment. The limitation of classical random graph models is low variance in parameters, while scale free networks are the natural, expected result of real-world variance. • Randomly stopped linking model generates scale free networks. • Scale free networks expected from any Bernoulli process with high variance. • Preferential attachment and growth not needed for scale free networks. • Heavy-tailed degree distributions come from mixture of geometric distributions. [ABSTRACT FROM AUTHOR]
ISSN:03784371
DOI:10.1016/j.physa.2022.127588