Scale-free percolation in continuous space: quenched degree and clustering coefficient - Archive ouverte HAL
Article Dans Une Revue Journal of Applied Probability Année : 2021

Scale-free percolation in continuous space: quenched degree and clustering coefficient

Joseba Dalmau

Résumé

Abstract Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuous-space version of scale-free percolation introduced in [14]. This is an undirected inhomogeneous random graph whose vertices are given by a Poisson point process in $\mathbb{R}^d$ . Each vertex is equipped with a random weight, and the probability that two vertices are connected by an edge depends on their weights and on their distance. Under suitable conditions on the parameters of the model, we show that, for almost all realizations of the point process, the degree distributions of all the nodes of the graph follow a power law with the same tail at infinity. We also show that the averaged clustering coefficient of the graph is self-averaging . In particular, it is almost surely equal to the annealed clustering coefficient of one point, which is a strictly positive quantity.
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Dates et versions

hal-03943091 , version 1 (17-01-2023)

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Joseba Dalmau, Michele Salvi. Scale-free percolation in continuous space: quenched degree and clustering coefficient. Journal of Applied Probability, 2021, 58 (1), pp.106-127. ⟨10.1017/jpr.2020.76⟩. ⟨hal-03943091⟩
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