  Many important real-world networks manifest "small-world" properties such as
scale-free degree distributions, small diameters, and clustering. The most
common model of growth for these networks is "preferential attachment", where
nodes acquire new links with probability proportional to the number of links
they already have. We show that preferential attachment is a special case of
the process of molecular evolution. We present a new single-parameter model of
network growth that unifies varieties of preferential attachment with the
quasispecies equation (which models molecular evolution), and also with the
Erdos-Renyi random graph model. We suggest some properties of evolutionary
models that might be applied to the study of networks. We also derive the form
of the degree distribution resulting from our algorithm, and we show through
simulations that the process also models aspects of network growth. The
unification allows mathematical machinery developed for evolutionary dynamics
to be applied in the study of network dynamics, and vice versa.
