Self-Reinforcing Success

Networks have their own logic. When you connect all to all, curious things happen.

Mathematics says the sum value of a network increases as the square of the number of members. In other words, as the number of nodes in a network increases arithmetically, the value of the network increases exponentially.* Adding a few more members can dramatically increase the value for all members.

[*I use the vernacular meaning of “exponential” to mean “explosive compounded growth.” Technically, n2 growth should be called polynomial, or even more precisely, a quadractic; a fixed exponent (2 in this case) is applied to a growing number n. True exponential growth in mathematics entails a fixed number (say 2) that has a growing exponent, n, as in 2n. The curves of some polynomials and exponentials look similar, except the exponential is even steeper; in common discourse the two are lumped together.]

This amazing boom is not hard to visualize. Take 4 acquaintances; there are 12 distinct one-to-one friendships among them. If we add a fifth friend to the group, the friendship network increases to 20 different relations; 6 friends makes 30 connections; 7 makes 42. As the number of members goes beyond 10, the total number of relationships among the friends escalates rapidly. When the number of people (n) involved is large, the total number of connections can be approximated as simply n X n, or n2. Thus a thousand members can have a million friendships.

The magic of n2 is that when you annex one more new member, you add many more connections; you get more value than you add. That’s not true in the industrial world. Say you owned a milk factory, and you had 10 customers who bought milk once a day. If you increased your customer base by 10% by adding one new customer, you could expect an increase in milk sales of 10%. That’s linear. But say, instead, you owned a telephone network with 10 customers who talked to each other once a day. Your customers would make about n2 (102), or 100 calls a day. If you added one more new customer, you increased your customer base by 10%, but you increased your calling revenue by a whopping 20% (since 112 is 20% larger than 102). In a network economy, small efforts can lead to large results.



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