Before revision:  This ambiguity is a result of the model's tight relation with the field of unequal probability random sampling , which dictates the exact process of edge creation after a newborn node has been added. In this work, we identify the ambiguity, assess its impact and propose a more precise definition of the Barabasi-Albert model that is expressed as an application of unequal probability random sampling  .
After revision:  This ambiguity is a result of the model's tight relation with the field of 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 Barabasi-Albert model that is expressed as an application of unequal probability random sampling .