  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.
