(Hat tip for prompting today’s post goes to The Bear)
Metcalfe’s Law tells us that the value of a network increases (roughly) at the square of the number of connections*.
If you add a single node to a network of two, you add two new connections.
Add one more node (the fourth), and you add three new connections.
Here’s a nice illustration via Twitter:
That’s how it works when you count only peer-to-peer (one-to-one) connections. But as Kevin Kelly points out, there are multiple layers of possible group connections too, which add further value:
In fact, n2 underestimates the total value of network growth. As economic journalist John Browning notes, the power of a network multiplies even faster than this.
Metcalfe’s observation was based on the idea of a phone network. Each telephone call had one person at each end; therefore the total number of potential calls was the grand sum of all possible pairings of people with phones. But online networks, like personal networks in real life, provide opportunities for complicated three-way, four-way, or many-way connections.
You can not only interact with your friend Charlie, but with Alice and Bob and Charlie at the same time. The experience of communicating simultaneously with Charlie’s group in an online world is a distinct experience, separate in its essential qualities, from communicating with Charlie alone.
Therefore, when we tally up the number of possible connections in a network we have to add up not only all the combinations in which members can be paired, but also all the possible groups as well. These additional combos send the total value of the network skyrocketing. The precise arithmetic is not important. It is enough to know that the worth of a network races ahead of its input.Kevin Kelly – New Rules for the New Economy
So far, so good, but network value is more complex than this – more next time.
*More specifically, adding a new node n to a network adds (n-1) new connections so that: “the number of unique possible connections in a network of n nodes can be expressed mathematically as the triangular number n ( n − 1 ) / 2, which is asymptotically proportional to n2.” (wikipedia)