Journal of Statistical Physics, Vol. 114, Nos. 5/6, March 2004. p. 1399-1416.
We formulate a simple edge generation rule based on an inverse like mass action principle for random graphs over a structured vertex set. We show that under very weak assumptions on this structure one obtains a scale free distribution for the degree. We furthermore introduce and study a ‘‘my friends are your friends’’ local search principle which makes the clustering coefficient large.