Tree and forest weights and their application to nonuniform random graphs

DOI10.1214/aoap/1029962602zbMath0930.05031OpenAlexW2068381506MaRDI QIDQ1296594

Brian D. Jones, Boris G. Pittel, Joseph S. Verducci

Publication date: 9 February 2000

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

Full work available at URL: https://doi.org/10.1214/aoap/1029962602

zbMATH Keywords

eigenvaluesspanning treesMaxwell's rulespectral graphKirchhoff matrixrandom rooted forestsparse random graph modeltotal weighttree polynomialtree-weight function

Mathematics Subject Classification ID

Trees (05C05) Random graphs (graph-theoretic aspects) (05C80)

Related Items

Perfect sampling methods for random forests, Forest matrices around the Laplacian matrix

Cites Work

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• A bound for the complexity of a simple graph
• Exponential models for directional data
• An upper bound for the number of spanning trees of a graph
• Probabilistic bounds on the coefficients of polynomials with only real zeros
• Matching behaviour is asymptotically normal
• A combinatorial Laplacian with vertex weights
• Theory of monomer-dimer systems
• Gibbs' Measures on Combinatorial Objects and the Central Limit Theorem for an Exponential Family of Random Trees
• Poisson convergence and random graphs
• On tree census and the giant component in sparse random graphs
• On colouring random graphs
• Cliques in random graphs
• Monotonicity of permanents of doubly stochastic matrices
• The Structure of a Random Graph at the Point of the Phase Transition
• The birth of the giant component
• Stirling Behavior is Asymptotically Normal
• Random Graphs
• Combinatorial Algebra and Random Graphs
• Asymptotic Formulas for the Probability of k-Connectedness of Random Graphs
• Inequalities: theory of majorization and its applications
• A normal law for matchings