Metcalfe’s Law is Wrong (2006)
spectrum.ieee.org
spectrum.ieee.org
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...
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.
[1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...
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_...
[1] https://www.quantamagazine.org/scant-evidence-of-power-laws-...
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.
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.
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.
If you liked this one, also read Content is not King