  The Barabasi-Albert model is a very popular model for creating random
scale-free graphs. Despite its widespread use, there is a subtle ambiguity in
the definition of the model and, consequently, the dependent models and
applications. 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.
