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April 01, 2005

A really fascinating result from Andrew Odlyzko and Benjamin Tilly, per CNet:
"The fundamental fallacy underlying Metcalfe's (Law) is in the assumption that all connections or all groups are equally valuable," the researchers report. [...] The researchers propose a less dramatic rule of thumb: the value of a network with n members is not n squared, but rather n times the logarithm of n. That means, for example, that the total value of two networks with 1,048,576 members each is only 5 percent more valuable together compared to separate. Metcalfe's Law predicts a 100 percent increase in value by merging the networks.
This is most immediately useful conclusion:
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.
That could be applied to peer-to-peer networks in this way -- when a member of an established cluster has a request for a new connection, it should evaluate the relative size of the cluster that the new connection is in. New nodes would be forced to join small clusters at first, and small clusters would be forced to join other small clusters.

Via the weblog of Lucas Gonze