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Large components in the subcritical Norros-Reittu model
Citation Link: https://doi.org/10.15480/882.14996
Publikationstyp
Journal Article
Date Issued
2025-01-11
Sprache
English
TORE-DOI
Journal
Citation
Extremes (in Press): (2025)
Publisher DOI
Scopus ID
The Norros-Reittu model is a random (multi-)graph with n vertices and i.i.d. weights assigned to them. The number of edges between any two vertices follows an independent Poisson distribution whose parameter is increasing in the weights of the two vertices. Choosing a suitable weight distribution leads to a power-law behaviour of the degree distribution as observed in many real-world complex networks. We study this model in the subcritical regime, i.e. in the absence of a giant component. For each component, we count all its vertices to determine the component sizes and show convergence of the corresponding point process of (rescaled) component sizes to a Poisson process. More generally, one can also count only specific vertices per component, like leaves. From this one can deduce asymptotic results on the size of the largest component or the maximal number of leaves in a single component. The results also apply to the Chung-Lu model and the generalised random graph.
Subjects
Norros-Reittu model | Poisson process convergence | (extremal) Counting statistics | Order statistics | Subcritical regime | Power law | Rank-1 inhomogeneous random graphs
DDC Class
519: Applied Mathematics, Probabilities
003: Systems Theory
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s10687-025-00504-9.pdf
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