Electronic Journal of Probability

Fixed speed competition on the configuration model with infinite variance degrees: unequal speeds

Enrico Baroni, Remco van der Hofstad, and Júlia Komjáthy

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We study competition of two spreading colors starting from single sources on the configuration model with i.i.d. degrees following a power-law distribution with exponent $\tau\in (2,3)$. In this model two colors spread with a fixed but not necessarily equal speed on the unweighted random graph.  We show that if the speeds are not equal, then the faster color paints almost all vertices, while the slower color can paint only a random subpolynomial fraction of the vertices. We investigate the case when the speeds are equal and typical distances in a follow-up paper.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 116, 48 pp.

Received: 22 August 2014
Accepted: 1 November 2015
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs [See also 60B20] 05C82: Small world graphs, complex networks [See also 90Bxx, 91D30] 90B15: Network models, stochastic 91D30: Social networks

Random networks configuration model competition power law degrees typical distances co-existence

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Baroni, Enrico; Hofstad, Remco van der; Komjáthy, Júlia. Fixed speed competition on the configuration model with infinite variance degrees: unequal speeds. Electron. J. Probab. 20 (2015), paper no. 116, 48 pp. doi:10.1214/EJP.v20-3749. https://projecteuclid.org/euclid.ejp/1465067222

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