A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The critical phase for random graphs with a given degree sequence
Combinatorics, Probability and Computing
A new approach to the giant component problem
Random Structures & Algorithms
The probability that a random multigraph is simple
Combinatorics, Probability and Computing
Component behavior near the critical point of the random graph process
Random Structures & Algorithms
A critical point for random graphs with a given degree sequence
Random Structures & Algorithms
SIR epidemics on random graphs with a fixed degree sequence
Random Structures & Algorithms
Tail bounds for the height and width of a random tree with a given degree sequence
Random Structures & Algorithms
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We consider a random graph on a given degree sequence D, satisfying certain conditions. Molloy and Reed defined a parameter Q = Q(D) and proved that Q = 0 is the threshold for the random graph to have a giant component. We introduce a new parameter R = R( \documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}\mathcal {D}\end{align*} \end{document} **image**) and prove that if |Q| = O(n-1/3R2/3) then, with high probability, the size of the largest component of the random graph will be of order Θ(n2/3R-1/3). If |Q| is asymptotically larger than n-1/3R2/3 then the size of the largest component is asymptotically smaller or larger than n2/3R-1/3. Thus, we establish that the scaling window is |Q| = O(n-1/3R2/3). © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2012 Wiley Periodicals, Inc.