
Scant Evidence of Power Laws Found in Real-World Networks - yarapavan
https://www.quantamagazine.org/scant-evidence-of-power-laws-found-in-real-world-networks-20180215/
======
jboggan
In grad school scale-free networks were the soup du jour and my advisor was
hammering on me to show that the human metabolic networks I studied had that
property. "Guaranteed paper in Nature, get on it!", he exhorted. I sensed
folks were not using the right statistical tests to show that distributions
were scale-free (hint, doing a log-log-plot and doing linear regression to get
a slope does _not_ give you the base of the power law if there is no power law
in the first place) and found a few notes on homepages that this was the case,
but no publications (this was 2006 or so).

There seems to be an attitude in the physical sciences that math is there as
sort of a glaze or condiment you can throw on top of bad data to make it
palatable. I didn't make many friends in the biology department by telling
them their pet model they'd based their careers off of wasn't only bolstered
by $trendy_math_analysis but actually weakened by it. People seemed less
interested in truth and more interested in appearance and publication
prestige.

~~~
mcguire
Speaking as a statistically-impaired person, how do you determine if you have
a power law?

~~~
curuinor
MLE, then vuong's test against alternatives. The linked paper is just vuong's
test against alternatives.

~~~
stuartaxelowen
Might want to try that again...

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cossatot
Always a good time to re-read Cosma Shalizi's classic "So You Think You Have a
Power Law — Well Isn't That Special?"
([http://bactra.org/weblog/491.html](http://bactra.org/weblog/491.html))

~~~
dmix
> that I have long had a thing about just how unsound many of the claims for
> the presence of power law distributions in real data are, especially those
> made by theoretical physicists, who, with some honorable exceptions, learn
> nothing about data analysis. (I certainly didn't.)

Statistics really needs to be a fundamental skill taught in all sciences (or
any field involved in research/studies) as 101 courses as math and writing
are.

It's amazing how much time/energy is wasted in research, across a wide swath
of fields, because the ultimate analysis lack a strong fundamental grasp of
statistics and data analysis.

I want to pull my hair out every time I read a Wikipedia article documenting
the historical back/forth of a particular social science... where the status
quo of knowledge is repeatedly discredited based on a biased manipulation or
simply a poor grasp of analyzing complex multi-faceted data.

~~~
rootw0rm
I completely agree. You can be a genius in your field, but mess things up when
it comes to basic statistics. it can be surprisingly easy to make major
errors. analyzing your own data is a fundamental skill that not only affects
how you present your own research, but how you learn from and perform your
research.

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tw1010
I love when facts contradict socially propagated truth, and we actually change
our minds as a consequence. That update mechanism is one of the biggest
sources of faith in humanity I can think of.

~~~
otakucode
Any time I hear a very socially useful truth proposed, I get very wary.
History is littered with ideas that were proclaimed to be true mostly only
because it would be very useful if it were true. It's certainly no guarantee
of illegitimacy, but if an idea comes along that basically says "hey, you know
how your society likes to do X? Turns out that's the best!" I immediately
enter high-skepticism mode. Everything from leaded gasoline to eugenics to the
Industrial Revolutions views on the dangers of masturbation can be laid at the
feet of people who so desperately wanted something to be true that they
skimped on rigor and ended up leaving unimaginable suffering in their wake.
When the doctor (I can never recall his name!) suggested other doctors wash
their hands between performing autopsies and delivering babies, he was
insulted and rejected, as the idea that doctors who wanted desperately to help
their patients were responsible for the astronomically high rate of death of
both mothers and infants was offensive. This is the opposite side of that
coin.

~~~
dredmorbius
That's effectively Appeal to Consequences fallacy, though in both its usual
(false rejection of an inconvenient truth) and inverse (false support of an
appealing falsehood) forms.

That's a useful counter-bias to have, though not an infallible one.

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otakucode
This would be tremendously comforting. After reading the book 'Linked', I have
been worried. It presents a possibility that I hope no one is immoral enough
to pursue. If it's claims of how social networks cluster, and how both
important and fragile the most critical edges in those networks are in terms
of enabling the society-wide spread of information/viewpoints/etc are all
true.... it opens a very dangerous door.

In the book, they claim that something like 'Six Degrees of Kevin Bacon' works
not because of those heavily-connected nodes, but primarily because of nodes
which bridge mostly-disconnected clusters. So like a member of a biker gang
who plays bridge with his elderly aunts knitting circle on Sundays would be an
example of that. Ideas can flow from the group of bikers to the group of
elderly knitters pretty much only through him. And almost by necessity, those
links are weak. Once broken, for information to travel from one of those
groups to the other immediately becomes extremely difficult.

So conjecture that there were an organization that had the ability to observe
the social network of peoples communications. Conjecture that they also felt
that they had a mandate to protect the status quo, at least on the largest
scale, and to do what was within their power to prevent things like widespread
social unrest, formation of disruptive political movements, etc. If they had
the ability to interfere with those communication networks even in a very mild
way, they could affect the most successful and quiet oppression in history. By
bouncing a few emails, dropping a few packets here and there, communication
between these weak links would break down pretty easily. And once mostly-
connected clusters only talk amongst themselves primarily, it becomes
fundamentally impossible for widespread social change to occur.

Now this is a very 'blind' approach, of course. You don't get to pick which
ideas get isolated and which are permitted to spread. But, you do gain a
guarantee that even if an idea is very powerful, it can never spread far
enough fast enough to gain widespread acceptance. Sure there might be "large
groups" that get very loud about it... but they wouldn't have an 'inside man'
to introduce the idea in ways acceptable to the mostly-disconnected group, so
it simply wouldn't spread. I've been wondering for several years now if this
kind of manipulation would leave telltale fingerprints.

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jkh1
This is not new, at least for biological networks. For example, see this paper
by Lima-Mendez and van Helden: The powerful law of the power law and other
myths in network biology:
[http://pubs.rsc.org/en/Content/ArticleLanding/2009/MB/b90868...](http://pubs.rsc.org/en/Content/ArticleLanding/2009/MB/b908681a#!divAbstract)
and several blog posts by Lior Pachter:
[https://liorpachter.wordpress.com/2014/02/10/the-network-
non...](https://liorpachter.wordpress.com/2014/02/10/the-network-nonsense-of-
albert-laszlo-barabasi/)

------
darkerside
For someone unfamiliar with power laws and scale in networks, that
introduction has me totally bamboozled with multiple repeating negatives.

A scale-free network is one that follows power laws, which manifests as having
specific hubs that are much more interconnected than others.

A random network does not follow power laws. Hubs and edges are distributed
relatively evenly.

Is that right?

~~~
hammock
Scale-free: distribution of connections follows power law across hubs. Other
type: it doesnt

~~~
esrauch
But "it doesn't" can include things that are both distrubuted with fatter or
thinner tails?

And if it is normally distrubuted below some range, and then power law above
that it also wouldn't be scale free under this paper?

~~~
marcosdumay
For the first question, yes. "Not power law" means anything else.

But I am quite confused on what you mean with power laws "above" or "below"
some range.

~~~
esrauch
It seems that the reason power laws are important is the frequency of
arbitrarily large values, and the implications those have on data processing.

Under a definition that strict it doesn't sound useful: imagine the most
common degree / # of connections is 10 and 5 is less popular: isn't that
already not a power law? Regardless of how the distribution behaves for degree
100, 1000, etc.

It seems like under many models you have some unimportant distribution of low-
degree connections and then close to a power law distribution if you consider
above some threshold: in terms of algorithm selection and design under those
conditions the dominating factor seems like it can typically still be just the
frequency of large degrees which can still be close to a power law and
rejected as one by this paper, right?

~~~
hammock
Yeah , I sort of agree that practically power laws are pretty useful, even if
they are approximators. I think the paper is trying to say though, the same
people (including myself) who use power law to generate these models often say
that these processes are actually power law processes. When in fact they may
not be. Which is surprising to me (Zipfs law and all of that)

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EGreg
I think Metcalfe's law is a bit overstated. Logic seems to suggest it starts
out close to exponential but eventually becomes more like log n. Because each
participant only has X amount of friends, that they derive benefit from.

For network of one-to-many broadcasts it may be more like n * k where k is the
number of active broadcasters.

~~~
dredmorbius
See Odlyzko-Tilly, "A Refutation of Metcalfe's Law".

[https://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf](https://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf)

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svat
A classic from Lior Pachter (not mentioned in the article) from 2014:
[https://liorpachter.wordpress.com/2014/02/10/the-network-
non...](https://liorpachter.wordpress.com/2014/02/10/the-network-nonsense-of-
albert-laszlo-barabasi/)

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dforrestwilson
What are the implications here for internet service providers and the big
social networking companies?

~~~
politician
For social networking companies, I believe that it means targeting influencers
to take advantage of their networks' coverage is much less powerful than first
thought. An advertiser won't expect to be able to steer dollars towards just a
few of the truly deeply connected influencers and gain outsized rewards;
instead, they'll have to target lots of influencers, reducing the ROI of the
project.

~~~
oakridge
Even more than that, the structure of these networks imply that targeting
influencers may be ineffective. There's an interview [0] with Duncan Watts
discussing this.

[0] Is the Tipping Point Toast? [https://www.fastcompany.com/641124/tipping-
point-toast](https://www.fastcompany.com/641124/tipping-point-toast)

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hammock
Now, why do so many systems seem to follow log-normal??

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yarapavan
A central claim in modern network science is that real-world networks are
typically "scale free," meaning that the fraction of nodes with degree k
follows a power law, decaying like k−α, often with 2<α<3\. However, empirical
evidence for this belief derives from a relatively small number of real-world
networks. We test the universality of scale-free structure by applying state-
of-the-art statistical tools to a large corpus of nearly 1000 network data
sets drawn from social, biological, technological, and informational sources.
We fit the power-law model to each degree distribution, test its statistical
plausibility, and compare it via a likelihood ratio test to alternative, non-
scale-free models, e.g., the log-normal. Across domains, we find that scale-
free networks are rare, with only 4% exhibiting the strongest-possible
evidence of scale-free structure and 52% exhibiting the weakest-possible
evidence. Furthermore, evidence of scale-free structure is not uniformly
distributed across sources: social networks are at best weakly scale free,
while a handful of technological and biological networks can be called
strongly scale free. These results undermine the universality of scale-free
networks and reveal that real-world networks exhibit a rich structural
diversity that will likely require new ideas and mechanisms to explain.

Paper referred:
[https://arxiv.org/abs/1801.03400](https://arxiv.org/abs/1801.03400)

~~~
EGreg
It reminds me a bit of how Romans used to build their ships by exactly scaling
up everything.

However, it is now known that, for larger ships, the proportions should be
different.

~~~
dmreedy
I've always been a fan of Haldane's treatment of the matter:
[http://irl.cs.ucla.edu/papers/right-
size.html](http://irl.cs.ucla.edu/papers/right-size.html)

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tzahola
“Power laws” are the golden ratio of network science.

