Complexity_ A Guided Tour - Melanie Mitchell [109]
Four days after the folders were sent to a group of starting persons in Kansas, an instructor at the Episcopal Theological Seminary approached our target person on the street. “Alice,” he said, thrusting a brown folder toward her, “this is for you.” At first she thought he was simply returning a folder that had gone astray and had never gotten out of Cambridge, but when we looked at the roster, we found to our pleased surprise that the document had started with a wheat farmer in Kansas. He had passed it on to an Episcopalian minister in his home town, who sent it to the minister who taught in Cambridge, who gave it to the target person. Altogether, the number of intermediate links between starting person and target amounted to two!
In his most famous study, Milgram found that, for the letters that made it to their target, the median number of intermediate acquaintances from starter to target was five. This result was widely quoted and is the source of the popular notion that people are linked by only “six degrees of separation.”
Later work by psychologist Judith Kleinfeld has shown that the popular interpretation of Milgram’s work was rather skewed—in fact, most of the letters from starters never made it to their targets, and in other studies by Milgram, the median number of intermediates for letters that did reach the targets was higher than five. However, the idea of a small world linked by six degrees of separation has remained as what may be an urban myth of our culture. As Kleinfeld points out,
When people experience an unexpected social connection, the event is likely to be vivid and salient in a person’s memory .... We have a poor mathematical, as well as a poor intuitive understanding of the nature of coincidence.
Stanley Milgram, 1933–1984. (Photograph by Eric Kroll, reprinted by permission of Mrs. Alexandra Milgram.)
So is it a small world or not? This question has recently received a lot of attention, not only for humans in the social realm, but also for other kinds of networks, ranging from the networks of metabolic and genetic regulation inside living cells to the explosively growing World Wide Web. Over the last decade questions about such networks have sparked a stampede of complex systems researchers to create what has been called the “new science of networks.”
The New Science of Networks
You’ve no doubt seen diagrams of networks like the one in figure 15.1. This one happens to be a map of the domestic flight routes of Continental Airlines. The dots (or nodes) represent cities and the lines (or links) represent flights between cities.
Airline route maps are an obvious example of the many natural, technological, and cultural phenomena that can usefully be described as networks. The brain is a huge network of neurons linked by synapses. The control of genetic activity in a cell is due to a complex network of genes linked by regulatory proteins. Social communities are networks in which the nodes are people (or organizations of people) between whom there are many different types of possible relationships. The Internet and the World Wide Web are of course two very prominent networks in today’s society. In the realm of national security, much effort has been put into identifying and analyzing possible “terrorist networks.”
FIGURE 15.1. Slightly simplified route map of Continental Airlines. (From NASA Virtual Skies: [http://virtualskies.arc.nasa.gov/research/tutorial/tutorial2b.html].)
Until very recently, network science was not seen as a field unto itself. Mathematicians studied abstract network structures in a field called “graph theory.” Neuroscientists studied neural networks. Epidemiologists studied the transmission of diseases