The value of a network is claimed to grow roughly with the square of the number of connected users.
Network value can grow faster than user count, but the specific n-squared valuation is a heuristic rather than an established law, and models such as n log n fit better in many settings. It nonetheless drove much of the valuation logic of the dot-com era.
In practice
- A messaging app is useless with three users and indispensable with three hundred, and no feature changed in between.
- A jobs board with fifty employers and no candidates has neither, and the first thousand of each are the whole difficulty.
- Possible explanations
- The explanation is combinatorial: the number of possible pairs of users grows with the square of their number, and the law treats every pair as equally valuable.
- In its favour
- Network value does grow faster than user count, which is the durable point, and the law captured why early network businesses were worth building before they were profitable.
- Against it
- Users do not value all connections equally, so the square overstates it; models closer to n log n fit measured data better, and the law was used to justify valuations in the dot-com period that did not survive.
- Standing
- The n-squared form is a heuristic rather than an established law; alternatives such as n log n fit better in many settings. Compare Odlyzko's law.
- Further reading
- Wikipedia
- Subject
- Networks & Collective Behavior
- Essay
- How connections shape what crowds do