two nodes are to be directly linked if they are both linked to a third. A relatively high clustering rate is one of the counterintuitive features of small-world networks. The short path length in small-world networks is similar to the situation in random networks. On the other hand, the high clustering coefficient is completely unlike that in random networks, but is more similar to that in regular networks.

This clustering property (you could call it the measure of “cliquishness”) is especially of interest in social networks. Since my sister Sue, for instance, has a friend Debby and a friend Janet, it is more likely than average that Debby and Janet also know each other. (They do.) “There is a tendency to form triangles, and you wouldn’t see that in random networks,” Strogatz pointed out.

Besides clustering coefficient and path length, another critical number is the average number of links connecting one node to another, known as the degree coefficient. (The “degree” of a node is the number of other nodes it is linked to.) As a node in the actor network, Kevin Bacon would be ranked very high in degree, being connected to so many others. Being well connected, after all, is what makes the average path length between Bacon and other actors so short. But in a shocking development, it turned out that Bacon is far from the most connected of actors. Taking the average number of steps to link to another actor as the gauge, he doesn’t even rank in the top 1,000!

It turns out, in fact, that Bacon’s true importance for networks had nothing to do with how special he is, but rather how typical he is. Many actors, like Bacon, serve as “hubs” connecting lots of other members of the acting community. And the existence of such hubs turns out to be a critical common feature of many real-world networks.

THE POWER OF SCALE FREEDOM

As of mid-2004, the actor leading the list as “most connected” (based on the average number of steps to link him with all the other actors) was Rod Steiger, at 2.679 steps. Bacon, at 2.95,



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement