How much more valuable is a network with 100 users than one with 50 users? If you know "Metcalfe's law", coined by Bob Metcalfe, inventor of the Ethernet networking system and founder of 3Com, you'll be saying "four times", but a new report says Metcalfe got it wrong. Three authors of a paper in IEEE Spectrum magazine say that's an overestimate - and responsible for some of the hyped stock valuations of the first Internet bubble. The claim has brought an annoyed response from Metcalfe himself, who insists that the new metric offered by the authors (which says that a network's value grows faster than the number of users, but not as fast as Metcalfe claims) is itself wrong. The difference is crucial to the venture capitalists investing billions of dollars in the new sites and services the average citizen wants to use. And if the IEEE authors are right, your online participation is now worth less than previously thought. Metcalfe's Law says that the value of a network rises with the square of the number of devices attached, while its cost grows linearly; so at some point, the benefit of being attached outweighs the cost. Metcalfe argued this to push Ethernet: while it was expensive to set up a network of two or three users, and not very useful, it didn't cost much more to extend the network to 10 or 20 or 200 users. Metcalfe asserted that while the cost of the network grew in a linear fashion, the value of the network grew by the square of the number of devices. So if a network of 1,000 users has a value of £1m, and that network is expanded to 2,000 users, Metcalfe's Law says its value will be £4m. The IEEE Spectrum authors - whose article appears under the uncompromising headline "Metcalfe's Law is Wrong" - blame that logic "at least in small part" for the huge stock valuations put on web companies in the first Internet bubble. They suggest that useful connections grow more slowly. "The fundamental flaw underlying ... Metcalfe's law is the assignment of equal value to all connections or all groups," they say, quoting Thoreau - who once remarked, about building a telegraph line to connect Maine and Texas, that "Maine and Texas, it may be, have nothing important to communicate". The authors note that if value really did grow quadratically, people with rival networks (say, instant messaging systems) would readily combine and make everybody better off. But they don't. "We propose, instead, that the value of a network of size n grows in proportion to n log(n)," they write. Now if you double the size of your £1m network of 1,000 users, its value becomes £2.1m, not £4m. Metcalfe - now a venture capitalist - argues that his law worked when he invented it, in the early 1980s. A better formulation could take other factors into account - including the idea that with too many users, a network's value starts to shrink, due to costs of network congestion, identity management, and security. After all, it's great if a network means you can email anybody. The downside? Anybody can spam you. No responsibility can be taken for the content of external Internet sites.