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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 oftheir degree $k$ and the square root of their respective birth time, then thedistribution 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 fordifferent 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 networkfalls into two universality classes depending on whether new nodes arrive withsingle edge ($m=1$) or with multiple edges ($m>1$).

Dynamic scaling, data-collapse and self-similarity in Barab\'{a}si-Albert networks