In the past weeks, I have received several requests to address the merits of the Anna D. Broido and Aaron Clauset (BC) preprint  and their fruitless search for scale-free networks in nature. The preprint’s central claim is deceptively simple: It starts from the textbook definition of a scale-free network as a network with a power law in the degree distribution . It then proceeds to fit a power law to 927 networks, finding that only 4% are scale-free. The author’s conclusion that ‘scale-free networks are rare,’ is turned into the title of the preprint, helping it to get maximal attention. It worked—Quanta magazine accepted its conclusions without reservations. AfterThe Atlantic carried the article, the un-refereed preprint received a degree of media exposure that the original discovery of scale-free networks never enjoyed.
While I saw the conceptual problems with the manuscript, I was convinced that the paper must be technically proficient. Yet, once I did dig into it, it was a real ride. If you have the patience to get to the end of this commentary, you will see where it fails at the conceptual level. But, we will learn that it also fails, repeatedly, at the technical level.
Love is All You Need
Clauset’s fruitless search for scale-free networks