Giant components in Kronecker graphs

Let \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath, amssymb} \pagestyle{empty} \begin{document} \begin{align*}n\in\mathbb{N}\end{align*} \end{document} **image** , 0 \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.