Ph.D. flashback of the day: scale-free networks

I was reading an article today from Quanta Magazine: Scant Evidence of Power Laws Found in Real-World Networks which refers to a posted article in arXiv: Scale-free Networks are Rare by Anna D. Broido and Aaron Clauset. And that gave me flashbacks of my Ph.D…

While, scale-free/power-law distributed networks weren’t really the main focus on my research, it did influence what I was doing, as it related to graph-structured databases, where a lot of that structure exists and affects scalability of your analysis. But, more importantly, it influenced a collaboration that I had with another researcher on the same department, Steve Morris. His actual interest was really on power-law distributed networks and his belief was that there was signal to be observed from when a network deviated from being power-law distributed.

During one Summer, we sat together and decided that the way researchers were claiming that everything was power-law distributed was by plotting it in a log-log scale and drawing a line through the points. We hypothesized that it was not a very good way to show that it followed the right distribution and we should have an actual statistical test. My proposal was to use bootstrapping and the Kolmogorov–Smirnov test. So we co-wrote a paper on it: Problems with Fitting to the Power-Law Distribution.

We didn’t have as much data to play with as the paper that I mentioned above, but we also did conclude that almost nothing was actually power-law distributed. And, until this date it’s the paper that I wrote with the most number of citations (622, according to Google Scholar).

We were onto something back then… Oh, well…