  We study Erd\"{o}s-R\'enyi random graphs with random weights associated with
each link. We generate a new ``Supernode network'' by merging all nodes
connected by links having weights below the percolation threshold (percolation
clusters) into a single node. We show that this network is scale-free, i.e.,
the degree distribution is $P(k)\sim k^{-\lambda}$ with $\lambda=2.5$. Our
results imply that the minimum spanning tree (MST) in random graphs is composed
of percolation clusters, which are interconnected by a set of links that create
a scale-free tree with $\lambda=2.5$. We show that optimization causes the
percolation threshold to emerge spontaneously, thus creating naturally a
scale-free ``supernode network''. We discuss the possibility that this
phenomenon is related to the evolution of several real world scale-free
networks.
