
Metcalfe’s Law is Wrong (2006) - hapnin
https://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong
======
nordsieck
I think one of the best ways to understand network scaling (in the human
sense) is the warrens and plazas metaphor [0]

Warrens are venues with relatively small size, that are relatively opaque to
the outside. In principle, there is no scalability limit to warrens, as
warrens scale horizontally.

Plazas are venues with relatively large size that are relatively transparent
to the outside. Plazas scale vertically, and so run into all sorts of size
based scaling difficulties [1][2].

I'd expect networks like facebook which are very warren-y to have a much lower
value growth curve relative to the number of nodes. While it's true that
Facebook has created plaza-ish features like Pages, the core function of the
network is explicitly warren-y, with a cap to the number of friends any
profile can have.

In contrast, a network like twitter should have a value growth curve much
closer to Metcalf's law since it is almost completely plaza-ish.

[0] [https://www.ribbonfarm.com/2010/10/27/warrens-plazas-and-
the...](https://www.ribbonfarm.com/2010/10/27/warrens-plazas-and-the-edge-of-
legibility/)

[1]
[https://en.wikipedia.org/wiki/Dunbar%27s_number](https://en.wikipedia.org/wiki/Dunbar%27s_number)

[2]
[https://pjammer.livejournal.com/61330.html](https://pjammer.livejournal.com/61330.html)

------
caseysoftware
Metcalfe lives here in Austin and is involved in the local startup community
in a variety of ways.

One time I asked him how he came up with the law and he said something close
to: "It's simple! I was selling network cards! If I could convince them it was
more valuable to buy more, they'd buy more!"

As an EE who studied networks, etc in college, it was jarring but audacious
and impressive.

 _He was either BSing all of us ~40 years ago or in that conversation a few
years ago.. but either way, he helped make our industry happen._

~~~
heisenbit
Build it and they will come. Scale it up and it will turn to gold. IPO before
reality catches up.

------
imglorp
Metcalfe is an interesting character, still sharp and full of stories. Ferriss
did a nice, non-technical, long form interview with him that covers his time
at Xerox and 3Com and what he learned about leadership and business. They do
discuss his law, if you want to hear it from the horse.

[https://tim.blog/2018/02/14/bob-metcalfe](https://tim.blog/2018/02/14/bob-
metcalfe)

------
QML
I'm surprised the Erdős–Rényi model [1] isn't mentioned in this article along
with Metcalfe's Law and Zipf’s Law. There's a nice phenomenon with random
graphs: if the probability of two users being connected > log n / n, then the
graph is "surely" connected.

[1]
[https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...](https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model)

~~~
abetusk
Erdos-Renyi random graphs aren't mentioned probably because they hold almost
no relevance to social graphs and networks, like the ones being addressed by
Metcalfe's and Zipf's law. Erdos-Renyi random graphs have a Gaussian degree
distribution (or maybe Poissonian degree distribution) [1] which effectively
makes the number of edges a proportion of the number of vertices with a narrow
band of variation as a result of the finite variance. Social networks tend to
have some type of power law or "long tailness" to them, giving them unbounded
variance of degree and often giving them unbounded mean degree [2] [3].

Another way to say this is Erdos-Renyi random graphs are not long tailed,
power law degree distributed or scale free, which Metcalf's law and Zipf
distributions address in one form or another.

[1]
[https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...](https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model#Properties_of_G\(n,_p\))

[2]
[https://en.wikipedia.org/wiki/Long_tail](https://en.wikipedia.org/wiki/Long_tail)

[3]
[https://en.wikipedia.org/wiki/Stable_distribution](https://en.wikipedia.org/wiki/Stable_distribution)

~~~
QML
After rereading this article [1], I’d have to agree the Erdos model is ill-
fitting — but still disappointed no model was mentioned.

[1] [https://www.quantamagazine.org/scant-evidence-of-power-
laws-...](https://www.quantamagazine.org/scant-evidence-of-power-laws-found-
in-real-world-networks-20180215/)

------
toss1
These 'laws' of network value address only the potential value -- each node
could make n*(n-1) connections.

However, the network will never actually make all of those connections. None
of us will ever call anything close to everyone on the telephone network,
contact everyone on FB or Twitter, etc. Yes, there is value in the larger
network of addressable nodes that could potentially be connected, but it seems
to me that the yield of connections made also counts.

So, the value of a network should first include the available resources of the
nodes connecting, such as time. A telephone network has a different value from
a broadcast network. The telephone users can only physically call other people
for 86400 seconds/day, etc., so the yield of connectsion made is capped. Vs a
broadcast network that can simultaneously reach millions, but only one-way.

Similarly, the friction in making connections needs to be considered. E.g., a
telephone network with speed dial has more net available connection time than
a network requiring everyone to talk to the operator and get literally patched
thru.

Search functions, and discover-ability also come into play. Having the White
Pages where everyone was listed in the US would have made its telephone
network much more valuable than a Russian network of exactly the same size
where no numbers were published. Similarly, DNS adds zero new connections to
the Internet, but makes it enormously more valuable.

Obviously, this lacks quantative measures, but these are the sorts of factors
I'd want to see in an improved algorithm.

~~~
EGreg
Very well said. One would probably have O(log N) potential partners for
activities they care about.

------
andreareina
I was initially skeptical about the _n log(n)_ , but the arguments are
persuasive. Specifically about not all connections being worth the same. That
they follow Zipf's law specifically is a minor point I think, the overall
shape seems right.

~~~
sitkack
> Specifically about not all connections being worth the same

Kicker right here. If don't know what makes a network interesting, it is best
to just add more links as fast as possible. In a network like Quora, they were
initially successful because they curated the link quality.

------
stretchwithme
I think you can't even trace all of the effects, so it can be neither proven
nor disproven. You would need to study something much simpler than human
beings.

And it might be more accurate to say the POTENTIAL is what scales. And this is
one more technology that some people don't exploit at all and that others make
the most of.

But it is right enough to describe the gist of the situation.

------
dmoy
Hah from the title I guessed this was an Odlyzko paper.

If you liked this one, also read Content is not King

------
beefman
My response to this article, written in 2006:

[http://lumma.org/microwave/#2006.08.23](http://lumma.org/microwave/#2006.08.23)

