Metcalfe proposes that the value of a network is proportional to the square of the number of nodes.
v(n)=n2
Simple maths shows that if you split a network into two, it halves the total value:
(n/2)2 + (n/2)2 = n2/4 + n2/4 = n2/2
This is why it is good that there is only one email network, and bad that there are so many Instant Messenger networks. It is why it is good that there is only one World Wide Web.
The term Web 2.0 was invented by a book publisher (O'Reilly) as a term to build a series of conferences around.
It conceptualises the idea of Web sites that gain value by their users adding data to them, such as Wikipedia, Facebook, Flickr, ...
By putting a lot of work into a website, you commit yourself to it, and lock yourself in to their data formats too.
This is similar to data lock-in with software. Moving comes at great cost.
There is no standard way of getting your data out of one Web 2.0 site to get it into another.
As an example, if you commit to a particular photo-sharing website, you upload thousands of photos, tagging extensively, and then a better site comes along. What do you do?
How do you decide which social networking site to join? Do you join several and repeat the work? I am currently being bombarded by emails from networking sites (LinkedIn, Dopplr, Plaxo, Facebook, MySpace, Hyves, Spock...) telling me that someone wants to be my friend, or business contact.
How about genealogy sites? You choose one and spend months
creating your family tree. The site then spots similar people in your tree on
other trees, and suggests you get together. But suppose a really important tree
is on another site?
How about if your chosen site closes down: all your work is lost. This happened with MP3.com for instance. And Stage6.
How about if your account gets closed down? There was someone whose Google account got hacked, and so the account got closed down. Four years of email lost, no calendar, no Orkut. Here is someone whose Facebook account got closed. Why? Because he was trying to download all the email addresses of his friends into Outlook.
These are all examples of Metcalfe's law in action.
Web 2.0 partitions the Web into a number of topical sub-Webs, and locks you in, thereby reducing the value of the network as a whole.
What should really happen is that you have a personal Website, with your photos, your family tree, your business details, and aggregators then turn this into added value by finding the links across the whole web.
Firstly and principally, machine readable Web pages. One of the technologies that can make this happen is RDFa.
You could describe it as a CSS for meaning: it allows you to add a small layer of markup to your page that adds machine-readable semantics.
It allows you to say "This is a date", "This is a place", "This is a person" (and anything else) and uniquely identify them on your web page.
When an aggregator comes to your Website, it should be able to see that this page represents (a part of) your family tree, and so on.
If a page has machine-understandable semantics, you can do lots more with it.
Rather than putting all your data on someone else's website, and the fact that it is there implying a certain semantics, you should put your own data on your own website with explicit semantics.
Then we can get the true web-effect, with its full Metcalfe value.