Ross Mayfield has an interesting post on Many-2-Many, Open Network Effects. In it, Ross wonders:

. . . I am continuing to wonder if Metcalfe's law is an adequate measure of network value when the network is a platform and the network is open. . .

[Using Feedburner's feed splicing as an example] Now open value added services are being spliced in such as Flickr for photos and Del.icio.us for social bookmarks. With less effort, authors can include new forms of content into their feed that provides. Readers then gain an incentive to switch to the new feed and can do so with nominal switching costs.

The value of the network grows in something closer to Reed's Law of group forming. . .

I think Ross is making an interesting point. And, I think there might be another way to look at how Metcalfe's Law applies, and how Reed's Law comes into play.

Perhaps, another way to look at Metcalfe's Law in this context is that each service acts as its own network. So, there is a Flickr network, and a del.icio.us network, and a blog network.

Each of us (say, with a blog that can plug into Flickr and/or del.icio.us) may act as nodes on one or more networks—and, when acting as a node on more than one, we may act as bridges between the networks.

I think, using this model, it's possible to see how these services are expanding value according to Metcalfe's Law (by adding more network nodes) with less than a linear increase in total users (i.e., each user accounts for more than one node on the combined inter-network).

Where I think Reed's Law comes into play is that the networks' support of group-forming is, in each bridge, also expanding according to Metcalfe's Law rather than just linearly. This suggests a law like:

the value of group-forming networks also grows at approximately the square of the number of networks interconnected

(So, hey, is this a new law?)

To try to picture it. Imagine: instead of two fax machines whose fax-machine-value is increased through interconnection, we have two group-forming networks whose group-forming-network-value is increased through interconnection.

Practically, this means that the number of participants in a group-forming inter-network is not the number of people, but the number of nodes—and each participant may appear as more than one node (possibly each expressing a different facet of the participants online identity).

Bottom line, with either of the Laws of Metcalfe or Reed: I think the open network / inter-network environment makes it possible for people to add-value more than once on the input side of the equation.

(Also of interest: Last year, I wrote an introduction to Metcalfe's and Reed's Laws for my co-workers. See my post: Relationship between technology, people, and value.)