  In studying network growth, the conventional approach is to devise a growth
mechanism, quantify the evolution of a statistic or distribution (such as the
degree distribution), and then solve the equations in the steady state (the
infinite-size limit). Consequently, empirical studies also seek to verify the
steady-state prediction in real data. The caveat concomitant with confining the
analysis to this time regime is that no real system has infinite size; most
real growing networks are far from the steady state. This underlines the
importance of finite-size analysis. In this paper, we consider the
shifted-linear preferential attachment as an illustrative example of
arbitrary-time network growth analysis. We obtain the degree distribution for
arbitrary initial conditions at arbitrary times. We corroborate our theoretical
predictions with Monte Carlo simulations.
