The Barab\'asi-Albert model is a popular scheme for creating scale-free graphs but has been previously shown to have ambiguities in its definition. In this paper we discuss a new ambiguity in the definition of the BA model by identifying the tight relation between the preferential attachment process and unequal probability random sampling. While the probability that each individual vertex is selected is set to be proportional to their degree, the model does not specify the joint probabilities that any tuple of $m$ vertices is selected together for $m>1$. We demonstrate the consequences using analytical, experimental, and empirical analyses and propose a concise definition of the model that addresses this ambiguity. Using the connection with unequal probability random sampling, we also highlight a confusion about the process via which nodes are selected on each time step, for which - despite being implicitly indicated in the original paper - current literature appears fragmented.

翻译：Barab\'asi-Albert 模型是创建无比例尺图的流行计划,但以前曾显示其定义含糊不清。 在本文中,我们讨论BA模型定义的新的模糊之处,方法是确定优惠附加程序与概率随机抽样之间密切的关系。虽然选择每个顶点的概率与它们的程度成比例,但该模型没有具体说明任何数额为百万美元的脊椎一起为$>1美元所选择的共同概率。我们用分析、实验和实证分析来说明其后果,并提出处理这种模糊的模型的简明定义。我们利用与不平等概率随机抽样的关联,我们还强调了对每个步骤选择节点的过程的混乱,尽管原始文件已暗示了这一点,但目前文献却显得支离破碎。