Network diagrams are a popular way of visualizing social and corporate relationships. Network theory has been used to model telecommunications performance and especially, the Internet. Communications networks increase in value as the number of connections increases. Metcalfe’s Law attempts to quantify the increased value.
Optimizing Metcalfe’s Law
For a network with n members, Metcalfe’s Law posits that the total value of that network is proportional to
n * (n-1). Metcalfe’s Law as applied to the Internet, and even to the telephone network, is only valid if all connections have equal value. This is incorrect. Some internet connections are hardly used and contribute limited value. Of course, there are reasons to connect everyone that are not based on monetary value! Rural electrification is an example.
Andrew Odlyzko’s article about Metcalfe’s Law (IEEE Spectrum, 2006) was written with a keen awareness of the 2000 dotcom bubble. Odlyzko demonstrated how Metcalfe’s Law’s applicability could be limited by the equal value assumption, among others. I read it, and wondered: What is the Internet’s optimal number of nodes and connections? When did the value of a larger Internet network start diminishing?
At some point, ISPs (Internet Service Providers) stopped charging users for access, as the business of delivering content became more valuable than providing greater network connectivity. AOL charged for service until 2002 or so.
I thought it would be helpful to begin with a timeline of Internet growth, by number of sites connected and corresponding events, as a starting point for determining incremental value. I searched for a streamlined history, but the best that I could find is provided by The Computer History Museum, and it isn’t quite linear. It also has a lot of technical detail that isn’t relevant for verifying Metcalfe’s Law. I decided to construct a timeline of dates and nodes, from which connectivity can be determined. I am writing this partly for myself, for reference purposes. (I don’t know how to value connectivity, not yet.)
In the beginning
In the beginning, the Internet had only two nodes. It was called the ARPANET. (more…)