  Barab\'asi-Albert model describes many different natural networks, often
yielding sensible explanations to the subjacent dynamics. However, finite size
effects may prevent from discerning among different underlying physical
mechanisms and from determining whether a particular finite system is driven by
Barab\'asi-Albert dynamics. Here we propose master equations for the evolution
of the degrees, links and triangles distributions, solve them both analytically
and by numerical iteration, and compare with numerical simulations. The
analytic solutions for all these distributions predict the network evolution
for systems as small as 100 nodes. The analytic method we developed is
applicable for other classes of networks, representing a powerful tool to
investigate the evolution of natural networks.
