@MISC{04thediameter, author = {}, title = {The Diameter of Sparse Random Graphs}, year = {2004} }

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Abstract

Abstract We derive an expression of the form c ln n \Sigma o(ln n) for the diameter of a sparse random graph with a specified degree sequence. The result holds a.a.s., assuming certain convergence and supercriticality conditions are met. The proof is constructive and yields a method for computing the constant c. For the random graph G n;p with np = \Theta (1) + 1, we solve for c in closed form.