  We investigate a model protein interaction network whose links represent
interactions between individual proteins. This network evolves by the
functional duplication of proteins, supplemented by random link addition to
account for mutations. When link addition is dominant, an infinite-order
percolation transition arises as a function of the addition rate. In the
opposite limit of high duplication rate, the network exhibits giant structural
fluctuations in different realizations. For biologically-relevant growth rates,
the node degree distribution has an algebraic tail with a peculiar rate
dependence for the associated exponent.
