The concept of network effects and Metcalfe’s Law is really important in technology so it’s useful to understand how a network’s value grows with each new user that joins the network.  Here’s an attempt at making the power of network effects really easy to digest:

Step 1: Take a look at these three pictures

Each of the lines represents a connection that adds value to the network.  Let’s say each line is worth a value of 1.  Below is a table that shows how the number of possible connections grow as you add another fax machine to the network:

The relationship between the number in column 1 and column 2 turns out to be:

This equation is “proportional to n ^2”. The easiest way to think about this is that as n gets bigger, there’s not much difference between [n x n] and [n x (n-1)].

And you can see how fast this grows if we show a chart going up to 100 fax machines:

That’s it!

This post was written by John Ryu, Partner at Scout Ventures. Follow him on Twitter.