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Power law random graphs. Loose definition: distribution is power-law if Over some range of values for some exponent Examples  Degree distributions of.

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Presentation on theme: "Power law random graphs. Loose definition: distribution is power-law if Over some range of values for some exponent Examples  Degree distributions of."— Presentation transcript:

1 Power law random graphs

2 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  …

3 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

4 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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