We offer an alternative proof, using the Stein-Chen method, of Bollob\'{a}s' theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices.

翻译：我们利用Stein-Chen方法，给出了Bollobás定理关于随机图极端度数分布的另一种证明。该证明还提供了极端度数向其渐近分布的收敛速率。在更一般的设定下，即每对顶点之间连边的概率依赖于顶点数量时，同一方法同样适用。