June 2015 First passage percolation on inhomogeneous random graphs
István Kolossváry, Júlia Komjáthy
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Adv. in Appl. Probab. 47(2): 589-610 (June 2015). DOI: 10.1239/aap/1435236989


In this paper we investigate first passage percolation on an inhomogeneous random graph model introduced by Bollobás et al. (2007). Each vertex in the graph has a type from a type space, and edge probabilities are independent, but depend on the types of the end vertices. Each edge is given an independent exponential weight. We determine the distribution of the weight of the shortest path between uniformly chosen vertices in the giant component and show that the hopcount, i.e. the number of edges on this minimal-weight path, properly normalized, follows a central limit theorem. We handle the cases where the average number of neighbors λ̃ n of a vertex tends to a finite λ̃ in full generality and consider λ̃ = ∞ under mild assumptions. This paper is a generalization of the paper of Bhamidi et al. (2011), where first passage percolation is explored on the Erdős-Rényi graphs.


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István Kolossváry. Júlia Komjáthy. "First passage percolation on inhomogeneous random graphs." Adv. in Appl. Probab. 47 (2) 589 - 610, June 2015. https://doi.org/10.1239/aap/1435236989


Published: June 2015
First available in Project Euclid: 25 June 2015

zbMATH: 1317.05176
MathSciNet: MR3360391
Digital Object Identifier: 10.1239/aap/1435236989

Primary: 05C80
Secondary: 60J85 , 90B15

Keywords: continuous-time multitype branching process , first passage percolation , hopcount , inhomogeneous random graph , shortest-weight path

Rights: Copyright © 2015 Applied Probability Trust


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Vol.47 • No. 2 • June 2015
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