The network nonsense of Albert-László Barabási

I work in a lab that directly competes with Barabási.

Barabási is seen as a mortal enemy and we try to discredit his work as often as possible, just as this article does.

But the truth is, the whole field is pretty much nonsense.

We try to apply network theory in a way which doesn't really apply. We make assumptions about biology that are trivially false. Any statistical results that reach significance fail to be significant on retesting. Any results which continue to be significant do not match the experimental data.

This field has not yet proven anything of true biological value.

I studied graph theory heavily in undergrad, started working in a genetics lab, and spent ~7 years in a bioinformatics PhD program focusing on biological networks. Barabasi was, at one time, the brightest contemporary star in my scientific pantheon.

Suffice to say, his publications (and most biological applications of network theory) are fairly meaningless beyond advancing careers. It's a case of cool sounding math that is misused and every PI wants to show that their tiny area of study is also scale-free/subject to cool network effects and therefore worthy of a publication pointing this out. The math is incredibly shoddy all around, and I was burned on several occasions by sticking up for actual scientific principles and pointing out when the math contradicted the assumptions they were trying to prove.

As an aside - this is my main distinction between Research and Science. Researchers do an excellent job of confirming their hypotheses via whatever model they can lay their hands on. Scientists falsify their hypotheses until no suitable model is left. I've met a lot of Researchers in my experience but couldn't truthfully tell you a true Scientist since the system discourages their existence.

Anyway, my advisor wanted me to SCALE-FREE ALL THE THINGS. The way that everyone gets a power-law in their system is (1) plot their system on a log axis, (2) do a linear fit, (3) voila the slope of the linear approximation is now the exponent of your scale-free power law system, no need to apply any statistical tests to show that your original system is actually exponential! And if you did want to take that extra step, just fiddle with the data until it does fit within your chosen margin of error.

I know several acclaimed mathematicians who have little stake in the arguments between network scientists, but who all seem to think that Barabasi's work is extremely low on good ideas.

I am inclined to believe that two decades from now, 'complex network research' will be in a much better state, and there'll be less room for the likes of Barabasi.

"Mathematics and the Internet: A Source of Enormous Confusion and Great Potential" http://www.ams.org/notices/200905/tx090500586p.pdf Is critical of scale-free networks of the preferential-attachment type, in particular of Barabasi's work. The paper is unusual for its polemic tone and for its name dropping. Researchers will trash each other in private--it is unusual to see this in print.

Much of the article is consumed with invidious comparisons of scale-free, preferential attachment network models of the internet with the authors’ own HOT (”highly organized/optimized tolerances/tradeoffs”) models: “In view of such a simple physical explanation of the origins of node degree variability in the Internet’s router-level topology, Stogartz’ question, paraphrasing Shakespeare’s Macbeth, ‘…power law scaling, full of sound and fury, signifying nothing?’ has a resounding affirmative answer.” The authors seem to suggest by this literary reference that a scale-invariant model of the Internet is a “tale told by an idiot.” This would not be lost on the readership of the Notices of the American Mathematical Society.

Its authors spare no opportunity to criticize their competition, as well as mathematicians and physicists generally, whom they regard as foppish, insular ivory tower aesthetes, whose nostrils are unacquainted with the bracing scent of an expertly soldered electrical connection.

Despite all of that, the authors are correct. I mention Doyle et al. because other authors have been critical of work on scale-free networks--this is not new. Doyle et al. warned about the misapplication of such networks to biology, though they mysteriously claimed that such failures of the scientific method "would reflect poorly on mathematics," as if mathematicians ought to be held responsible.

What I found more interesting than Pachter's analysis of the specific failings of the Barzel-Barabási paper is the more general implications for our scientific process. I have two parallel trains of thought:

1) We all know that we have scientific "celebrities" and that their work is often over-represented in high-quality journals (while dissenting viewpoints are often suppressed). There is nothing wrong with critizing the work of the celebrity du jour (or in this case, maybe, du décennie), but framing is everything and you will find more success in your scientific career with constructive and respectful criticism without resorting to ad hominem attacks such as "the emperor has no clothes". No one benefits from a bloody cage match.

2) Network science (like many interdisciplinary fields) has problems because many of its practitioners lack extensive knowledge of the systems, experimental challenges and core research methodologies of the fields or contexts to which they apply their developments. Success in such interdisciplinary fields is often incentivized and measured in a very narrow way and not associated with the primary goal of science -- useful and meaningful advances in our collective body of knowledge. You want to be at the top of your field, but presumably (or hopefully) you have more noble aspirations -- you want your work to have real meaning. But this lofty goal is challenged by the rapidly growing body of scientific work and the fracturing of science into siloed sub-fields. For example, finding the right set of peer reviewers for an interdisciplinary submission becomes increasingly challenging. Consequently, mistakes will be made, missed in the peer review process, and published. Dissenting opinions and followup work need to be given equal representation.

A case of so-called envy. The scale-free networks are nearly trivial and about as common as power law instances.

Barabási's works were the reason I entered science.