In the last chapter, we saw the importance of topology to functionality. In this and the next chapters, we will focus on generative models of network topology and reverse-engineering of network functionality. These are mathematical constructions that try to explain widespread empirical observations about social and technological networks: the “small world” property and the “scale free” property. We will also highlight common misunderstandings and misuse of generative models.

A Short Answer

Since Milgram's 1967 experiment, the small world phenomenon, or the six degrees of separation, has become one of the most widely told stories in popular science books. Milgram asked 296 people living in Omaha, Nebraska to participate in the experiment. He gave each of them a passport-looking letter, and the destination was in a suburb of Boston, Massachusetts, with the recipient's name, address, and occupation (stockbroker) shown. Name and address sound obvious, and it turned out that it was very helpful to know the occupation. The goal was to send this letter to one of your friends, defined as someone you knew by first name. If you did not know the recipient by first name, you had to send the letter via others, starting with sending it to a friend (one hop), who then sent it to one of her friends (another hop), until the letter finally arrived at someone who knew the recipient by first name and sent it to the recipient. This is illustrated in Figure 9.1.