### First passage percolation on inhomogeneous random graphs

#### Abstract

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.

#### Article information

Source
Adv. in Appl. Probab., Volume 47, Number 2 (2015), 589-610.

Dates
First available in Project Euclid: 25 June 2015

https://projecteuclid.org/euclid.aap/1435236989

Digital Object Identifier
doi:10.1239/aap/1435236989

Mathematical Reviews number (MathSciNet)
MR3360391

Zentralblatt MATH identifier
1317.05176

#### Citation

Kolossváry, István; Komjáthy, Júlia. First passage percolation on inhomogeneous random graphs. Adv. in Appl. Probab. 47 (2015), no. 2, 589--610. doi:10.1239/aap/1435236989. https://projecteuclid.org/euclid.aap/1435236989

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