  We show that the protein-protein interaction networks can be surprisingly
well described by a very simple evolution model of duplication and divergence.
The model exhibits a remarkably rich behavior depending on a single parameter,
the probability to retain a duplicated link during divergence. When this
parameter is large, the network growth is not self-averaging and an average
vertex degree increases algebraically. The lack of self-averaging results in a
great diversity of networks grown out of the same initial condition. For small
values of the link retention probability, the growth is self-averaging, the
average degree increases very slowly or tends to a constant, and a degree
distribution has a power-law tail.
