Metcalfe's Law Refuted

pdp0x14 writes "Cnet News reports on a powerful refutation of Metcalfe's Law (that the value of a network goes up with n^2 in the number of members). The academic paper is available at Southwest Missouri State University. Basically, the thesis is that not all the links in a network are equally valuable, so Metcalfe's argument that everyone can connect to everyone (n(n-1)/2 links, roughly n^2) is irrelevant. The authors propose nlog(n) instead, a much smaller increase."

Comments

Smaller Networks Win Out

[MankyD]

The last paragraph makes a very interesting point:

When two networks merge, "the smaller network gains considerably more than the larger one. This produces an incentive for larger networks to refuse to interconnect without payment, a very common phenomenon in the real economy," the researchers conclude.

Assuming their research holds true, adding 100 computers to 100,000 computers is pretty worthless for a big network - they get only a small gain compared to their starting value. The small network, on the other hand, has huge amounts compared to where they started.

It's common sense, of course, but worth taking note of.

Odlyzko's Arguments are Good

[filmmaker]

Especially the section on Zipf's Law.

Where I think Metcalf's Laws does apply is in an information network where no proprietary secrets exist. For instance, searching for technical documentation or a movie star's biography. In these instances, the value of the network, as measured by the immediacy with which one could obtain useful information by asking a question, is proportional to something on the order of n*n for n nodes.

Consider the network the top 10 search results in Google for all possible queries. Let's pretend for a moment that Google wasn't polluted with Spam. In this case, each node (search result) is providing a substantial amount of value to the network, although no matter how small or targeted the group, Zipf's Law will be observable to a degree.

Or consider if you had personal tele-access to every person on the planet and could ask any one of them a question at any time. Clearly here the value of the network is something on the order of n*n.

Most or all of Odlyzko's examples presupposed economic interests or constraints.

Re:Andrew Odlyzko is godlike

[Catiline]

No, I don't think the log scale wears down.

After all, it's the high end of that curve -- e.g. the anybody-to-anybody connection of the 'net -- that brings us things like wikipedia and Linux. IMO, when you start reaching scales "beyond mortal comprehension" (or at least everyday life) the growth isn't as much being able to connect to more individuals, but being able to have more specialized groupings and network those.

Even if the average person doesn't get very connected into the network, the value can still be quite high. Never forget the "Kevin Bacon" effect.