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It's commonly said that the value of a communication network is on the order of (n squared), so much so that it's become almost a cliche. But that value was arrived at a very long time ago, and is based on the assumption of using a fairly primitive and inflexible network, where only two parties my communicate with each other at any one time. Like so:


Table 1


That is, $ n^2 $. But what about a network in which three or more parties can communicate with each other at any one time? That network value then becomes on the order of $ 2^n $! A simple count of all the possible permutations will confirm this.