The Evolution of Random Graphs

Abstract

According to a fundamental result of Erdos and Renyi, the structure of a random graph GM changes suddenly when M n/2: if M = LcnJ and c < 2 then a.e. random graph of order n and since M is such that its 2 largest component has O(log n) vertices, but for c > 2 a.e. GM has a giant component: a component of order (1 ac + o(l))n where a, < 1. The aim of this… (More)

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