The Network Effect is not dependent on the network so much as the number of people that are using it. Two tin cans connected by a string is, in effect, a network, but not very powerful. The World Wide Web, well, that’s a network with a lot of connections.
Basically, the important aspect of the Network Effect as a force is kind of a Bandwagon. Not too long ago there were a few nerds that were connected on the web, then a few upstarts and very quickly, practically everyone and soon to be everything.
In terms of force, the network effect is a done deal on the Internet. Where else can you reach so many people (and devices) so fast. And, it is growing.
Not surprisingly, there is a pretty comprehensive article on Wikipedia on the Network Effect.