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:
That is, . 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 ! A simple count of all the possible permutations will confirm this.