Random networks with sublinear preferential attachment: the giant component

DOI10.1214/11-AOP697zbMath1260.05143arXiv1007.0899MaRDI QIDQ1942119

Peter Mörters, Steffen Dereich

Publication date: 15 March 2013

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.0899

zbMATH Keywords

clusterpower lawmultitype branching random walkBarabási-Albert modelscale-free networkErdős-Rényi modelgiant componentdynamic random graphnonlinear preferential attachment

Mathematics Subject Classification ID

Small world graphs, complex networks (graph-theoretic aspects) (05C82) Random graphs (graph-theoretic aspects) (05C80) Stochastic network models in operations research (90B15) Combinatorial probability (60C05)

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Typical Distances in Ultrasmall Random Networks ⋮ Near critical preferential attachment networks have small giant components ⋮ Likelihood theory for the graph Ornstein-Uhlenbeck process ⋮ Local weak convergence for PageRank ⋮ MATRIX-MFO tandem workshop: Stochastic reinforcement processes and graphs. Abstracts from the MATRIX-MFO tandem workshop held March 5--10, 2023 ⋮ Locality of random digraphs on expanders ⋮ On a preferential attachment and generalized Pólya's urn model ⋮ Scaling limits and influence of the seed graph in preferential attachment trees ⋮ A preferential attachment process approaching the Rado graph ⋮ The age-dependent random connection model ⋮ Fluctuations in a general preferential attachment model via Stein's method ⋮ Spatial preferential attachment networks: power laws and clustering coefficients ⋮ Distance evolutions in growing preferential attachment graphs ⋮ On dynamic random graphs with degree homogenization via anti-preferential attachment probabilities

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