The diameter of sparse random graphs

Authors:
Daniel Fernholz;Vijaya Ramachandran
Affiliations:
Department of Computer Sciences, University of Texas at Austin/ Texas;Department of Computer Sciences, University of Texas at Austin/ Texas
Venue:
Random Structures & Algorithms
Year:
2007

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Abstract

We derive an expression of the form c ln n + o(ln n) for the diameter of a sparse random graph with a specified degree sequence. The result holds asymptotically almost surely, assuming that certain convergence and supercriticality conditions are met, and is applicable to the classical random graph Gn,p with np = Θ(1) + 1, as well as certain random power law graphs. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007