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Published byMyron Adams Modified over 4 years ago

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Power law random graphs

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Loose definition: distribution is power-law if Over some range of values for some exponent Examples Degree distributions of graphs (web, « hollywood », protein interaction,…) Individual wealth City sizes …

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Barabasi-Albert « scale-free » random graphs So-called preferential attachment construction Initial graph: At time t, new node attached to by edge Where « anchor point » chosen according to Where : degree of in and

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Result: Barabasi-Albert random graph is power-law with exponent More precisely for fixed, nb of degree nodes in verifies Where for large [Proof: whiteboard, using analysis of averages + Azuma-Hoeffding inequality]

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