### A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections

A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections

Abstract. Metcalfe's Law states that the value of a communications network

is proportional to the square of the size of the network. It is widely accepted

and frequently cited. However, there are several arguments that this rule is a

signi¯cant overestimate. (Therefore Reed's Law is even more of an overestimate,

since it says that the value of a network grows exponentially, in the mathemat-

ical sense, in network size.) This note presents several quantitative arguments

that suggest the value of a general communication network of size n grows like

n log(n). This growth rate is faster than the linear growth, of order n, that,

according to Sarnof's Law, governs the value of a broadcast network. On the

other hand, it is much slower than the quadratic growth of Metcalfe's Law, and

helps explain the failure of the dot-com and telecom booms, as well as why net-

work interconnection (such as peering on the Internet) remains a controversial

issue.

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