Where do power laws come from?

Details Where do power laws come from? Where do power laws come from?

2007-02-15

arxiv.org/abs/math/0702463v1

Mathematics

Combinatorics

12 pages, 1 figure

Scientific paper

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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