# 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.