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Random processes with high variance produce scale free networks

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  • Johnston, Josh
  • Andersen, Tim

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.

Suggested Citation

  • Johnston, Josh & Andersen, Tim, 2022. "Random processes with high variance produce scale free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
  • Handle: RePEc:eee:phsmap:v:604:y:2022:i:c:s0378437122004058
    DOI: 10.1016/j.physa.2022.127588
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    References listed on IDEAS

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    1. Anna D. Broido & Aaron Clauset, 2019. "Scale-free networks are rare," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    2. Petter Holme, 2019. "Rare and everywhere: Perspectives on scale-free networks," Nature Communications, Nature, vol. 10(1), pages 1-3, December.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    4. Balanzario, Eugenio P. & Ramírez, Rosalva Mendoza & Ortiz, Jorge Sánchez, 2014. "The randomly stopped geometric Brownian motion," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 85-92.
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