Where do power laws come from?

2007/02/15 by Cooper, Joshua N., Lu, Lincoln
#05C80 #68R10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0702463

Abstract

What distribution of graphical degree sequence is invariant under ``scaling''? Are these graphs always power-law graphs? We show the answer is a surprising ``yes'' for sparse graphs if we ignore isolated vertices, or more generally, the vertices with degrees less than a fixed constant k. We obtain a concentration result on the degree sequence of a random induced subgraph. The case of hypergraphs (or set-systems) is also examined.

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