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Metcalfe's Law

The most famous heuristic for valuing a network is Metcalfe's Law which suggests that the value of a network is proportional to the square of the number of connected nodes (strictly n**2-n). That's because Metcalfe sees the potential uses of a network as having 1 to 1 conversations between nodes. Each further node which is connected to an n-node network adds n more possible conversations. Once again the telephone is a good example, as are email networks. If the telephone company makes money on every possible call, then they get income proportional to every possible combination.

But note that no telephone company is really in this position. New customers joining up can't possibly know or phone everyone else on the network so the value of the network is no longer growing at anything like proportional to n**2.

(Note : I'm using n**2 to mean n to the power 2)

So Metcalfe has a good point, but it's necessary to study the details of any particular network based business before assuming the law holds there.

Reed's Law

Another valuation put on networks is Reed's Law. Reed finds networks even more valuable than Metcalfe. Where Metcalfe considers all the possible 1 on 1 conversations, Reed sees networks as creating groups or communities. And every possible grouping of connected people is potentially valueable. Suppose Tom, Dick, Harry, Angela, Betty and Claire are all connected. There are 30 possible 1 on 1 conversations; but many more possible subgroups who might work together. There's the lads club consisting of Tom, Dick and Harry, and a similar girlie club of Angela, Betty and Claire. Then there's the X project which Dick, Angela, and Claire are involved in, and Harry and Betty's secret plan to elope together; meanwhile everyone except Tom is in the group planning a surprise party for his 40th birthday. And so on.

The number of possible groups within the n-node network is calculated as 2n (-1 if we exclude the group with 0 members) which, as n increases, quickly becomes far higher than n2. In the case of 6 people, Metcalfe's Law gives 30 1-1 conversations, Reed's Law gives 63 sub-groups.

Once again, whether a network has this value depends on the particulars. It is possible that, for example, software which allows the creation of mailing lists, discussion forums, and (some) other community activities has this character. On the other hand while it may be of value for a user to be a member of every possible grouping, it is also expensive. The user is likely to want to be charged for membership of the entire network (effectively the cost of the arc) and hence the creators of the network won't be able to cash in according to this kind of function.


The magic value of networks is about making connections between each node. One example which bears this out is negative. There is no network magic in broadcast. Many traditional media companies have wanted to take advantage of the internet; and as a cheap distribution chanel it is excellent. However with broadcast there is no scope for exploiting the value created by large numbers of people networked together. The value of customers scales with the number of customers. (Which is why nobody should have thought for a moment about making crazy, investment bets on content providers.) Nor does an online retailer, such as Amazon get much magic network dust.

Originally this page said AmazonCorp wasn't getting any special network magic. Unlike, say, EBay. But I later realized I was wrong : AmazonNetworkMagic

UmairHaque : Problems with AndrewOdlyzko's law :

Also :

See also :

  • RssAsAPlatform raises the interesting question of valuing the network of syndication feeds.

CategoryNetworks, CategoryEconomics