Theories on Network Value

Reed's Law of the Pack states:

the utility of large networks, particularly social networks, can scale exponentially with the size of the network.  

The reason for this is that the number of possible sub-groups of network participants is 2^N − N − 1, where N is the number of participants. This grows much more rapidly than either

• the number of participants, N, or

• the number of possible pair connections, N(N − 1)/2 (which follows Metcalfe's law).

...so that even if the utility of groups available to be joined is very small on a peer-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system.

So its a refined version of Metcalf's law, that highlights the value of subgroups.

But OTOH, Andrew Odlyzko disagrees, and claims network value grows like a logarithmic Meltcalf Law:

The fundamental flaw underlying both Metcalfe's and Reed's laws is in the assignment of equal value to all connections or all groups. 

Lots more on Value Networks at wikipedia.