Networks have their own logic. When you connect all to all, curious things happen.<\/p>\n
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.<\/strong><\/p>\n [*I use the vernacular meaning of “exponential” to mean “explosive compounded growth.” Technically, n2<\/sup> 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<\/em>. True exponential growth in mathematics entails a fixed number (say 2) that has a growing exponent, n<\/em>, as in 2n<\/sup>. The curves of some polynomials and exponentials look similar, except the exponential is even steeper; in common discourse the two are lumped together.<\/em>]<\/p>\n 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<\/em>) involved is large, the total number of connections can be approximated as simply n<\/em> X n<\/em>, or n2<\/sup>. Thus a thousand members can have a million friendships.<\/p>\n The magic of n2<\/sup> is that when you annex one more new member, you add many more connections; you get more value than you add.<\/span> 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<\/sup> (102<\/sup>), 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<\/sup> is 20% larger than 102<\/sup>). In a network economy, small efforts can lead to large results.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":" 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 … Continue reading