Scalable modeling of real graphs using Kronecker multiplication
Proceedings of the 24th international conference on Machine learning
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
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Let \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath, amssymb} \pagestyle{empty} \begin{document} \begin{align*}n\in\mathbb{N}\end{align*} \end{document} **image**, 0 K(n,α,γ,β) to be the graph with vertex set \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath, amssymb} \pagestyle{empty} \begin{document} \begin{align*}\mathbb{Z}_2^n\end{align*} \end{document} **image**, where the probability that u is adjacent to v is given by pu,v =α u⋅vγ(1-u)⋅(1-v)βn-u⋅v-(1-u)⋅(1-v). This model has been shown to obey several useful properties of real-world networks. We establish the asymptotic size of the giant component in the random Kronecker graph.© 2011 Wiley Periodicals, Inc. Random Struct. Alg.,2011 © 2012 Wiley Periodicals, Inc.