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Problems with classification, hypothesis testing, and estimator convergence in the analysis of degree distributions in networks
In their recent work "Scale-free networks are rare", Broido and Clauset
address the problem of the analysis of degree distributions in networks to
classify them as scale-free at different strengths of "scale-freeness." Over
the last two decades, a multitude of papers in network science have reported
that the degree distributions in many real-world networks follow power laws.
Such networks were then referred to as scale-free. However, due to a lack of a
precise definition, the term has evolved to mean a range of different things,
leading to confusion and contradictory claims regarding scale-freeness of a
given network. Recognizing this problem, the authors of "Scale-free networks
are rare" try to fix it. They attempt to develop a versatile and statistically
principled approach to remove this scale-free ambiguity accumulated in network
science literature. Although their paper presents a fair attempt to address
this fundamental problem, we must bring attention to some important issues in
it