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What type of phase transition do random graphs undergo as connectivity increases?

April 26, 2017connectivity graphs increases phase type undergo

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What type of phase transition do random graphs undergo as connectivity increases?

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Remark: See the glossary (above) for explanations of the terminology used below. For a more rigorous and detailed treatment of random graphs, see Bollobás (1985), Strogatz (2001), and Watts and Strogatz (1999). Erdös and Rényi (1960) were the first researchers to study how the connectivity of a random graph changes as a function of the number of its edges.