Subgraph counts in random graphs using incomplete U-statistics methods

DOI10.1016/0012-365X(88)90220-8zbMath0672.05072MaRDI QIDQ1119948

John C. Wierman, Krzysztof Nowicki

Publication date: 1988

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

random graphsubgraph countstrictly balanced graphweighted U-statistics

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80)

Related Items (16)

Edgeworth expansions for network moments ⋮ Motif-based tests for bipartite networks ⋮ When are small subgraphs of a random graph normally distributed? ⋮ On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics ⋮ Logarithmic Sobolev inequalities for finite spin systems and applications ⋮ Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon ⋮ A limit theorem for small cliques in inhomogeneous random graphs ⋮ Fluctuations of subgraph counts in graphon based random graphs ⋮ Local limit theorems for subgraph counts ⋮ Minimum variance rectangular designs for U-statistics. ⋮ On the number of weakly connected subdigraphs in random \(k\)NN digraphs ⋮ A local central limit theorem for triangles in a random graph ⋮ Anti-concentration for subgraph counts in random graphs ⋮ A central limit theorem for decomposable random variables with applications to random graphs ⋮ Incomplete U -statistics of permanent design ⋮ The asymptotic distributions of generalized U-statistics with applications to random graphs

Cites Work

• When are small subgraphs of a random graph normally distributed?
• Asymptotic normality of permutation statistics derived from weighted sums of bivariate functions
• Convergence rates for U-statistics and related statistics
• On the Berry-Esseen theorem for U-statistics
• The Berry-Esseen theorem for U-statistics
• Reduced U-statistics and the Hodges-Lehmann estimator
• Edgeworth expansions in nonparametric statistics
• Threshold functions for small subgraphs
• Limiting Behavior of Posterior Distributions when the Model is Incorrect
• A Class of Statistics with Asymptotically Normal Distribution
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