Nonstandard regular variation of in-degree and out-degree in the preferential attachment model

DOI10.1017/JPR.2015.15zbMath1343.60138arXiv1405.4882OpenAlexW1528687210MaRDI QIDQ2804420

Amy D. Willis, Don Towsley, Gennady Samorodnitsky, Phyllis Wan, Richard A. Davis, Sidney I. Resnick

Publication date: 29 April 2016

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.4882

zbMATH Keywords

scale-free networkspreferential attachment modelmultivariate heavy tails

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Extreme value theory; extremal stochastic processes (60G70) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (20)

Multivariate regular variation of discrete mass functions with applications to preferential attachment networks ⋮ Measuring reciprocity in a directed preferential attachment network ⋮ Risk in a Large Claims Insurance Market with Bipartite Graph Structure ⋮ The PageRank vector of a scale-free web network growing by preferential attachment ⋮ Asymptotic dependence of in- and out-degrees in a preferential attachment model with reciprocity ⋮ Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms ⋮ Consistency of Hill estimators in a linear preferential attachment model ⋮ Hidden regular variation under full and strong asymptotic dependence ⋮ Directed preferential attachment models: Limiting degree distributions and their tails ⋮ Random networks with heterogeneous reciprocity ⋮ Poisson edge growth and preferential attachment networks ⋮ Tauberian theory for multivariate regularly varying distributions with application to preferential attachment networks ⋮ PageRank on inhomogeneous random digraphs ⋮ Growth of common friends in a preferential attachment model ⋮ On the distribution of multiple power series regularly varying at the boundary point ⋮ Degree growth rates and index estimation in a directed preferential attachment model ⋮ Are extreme value estimation methods useful for network data? ⋮ Asymptotic normality of in- and out-degree counts in a preferential attachment model ⋮ Models with hidden regular variation: Generation and detection ⋮ On a Minimum Distance Procedure for Threshold Selection in Tail Analysis

Cites Work

• Unnamed Item
• Regularly varying measures on metric spaces: hidden regular variation and hidden jumps
• Tauberian theory for multivariate regularly varying distributions with application to preferential attachment networks
• Power Laws in Preferential Attachment Graphs and Stein's Method for the Negative Binomial Distribution
• Directed scale-free graphs
• Asymptotic independence and a network traffic model
• Heavy-Tail Phenomena

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