  In this article, we show that if each node of the Barab\'{a}si-Albert (BA)
network is characterized by the generalized degree $q$, i.e. the product of
their degree $k$ and the square root of their respective birth time, then the
distribution function $F(q,t)$ exhibits dynamic scaling $F(q,t\rightarrow
\infty)\sim t^{-1/2}\phi(q/t^{1/2})$ where $\phi(x)$ is the scaling function.
We verified it by showing that a series of distinct $F(q,t)$ vs $q$ curves for
different network sizes $N$ collapse onto a single universal curve if we plot
$t^{1/2}F(q,t)$ vs $q/t^{1/2}$ instead. Finally, we show that the BA network
falls into two universality classes depending on whether new nodes arrive with
single edge ($m=1$) or with multiple edges ($m>1$).
