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.
@article{arxiv.math/0702463,
title = {Where do power laws come from?},
author = {Joshua N. Cooper and Lincoln Lu},
journal= {arXiv preprint arXiv:math/0702463},
year = {2007}
}