bucket brigade that saves a house is a very simple social network. It is linear and has no branches: each person (except the first and last) is connected to two other people, the one in front and the one behind. For moving something like water long distances, this is a good way to be organized. But the optimal organization of one hundred people into a network depends very much on the task at hand. The best pattern of connections between a hundred people to put out a fire is different from the best pattern for, say, achieving a military objective. A company of one hundred soldiers is typically organized into ten tightly interconnected squads of ten. This allows each soldier to know all of his squad mates rather than just the grunt in front of him and the grunt behind him. The military goes to great lengths to help squad members know each other very well, so well in fact that they are willing to give their lives for one another.
Consider still another social network: the telephone tree. Suppose you need to contact a hundred people quickly to let them know that school is canceled. Before modern communications and the Internet, this was a challenge because there was no public source of up-to-the-minute information that everyone could access from their homes (though the ringing of church bells in the town square comes to mind). Instead, each person needed to be contacted directly. The telephone made this task much easier, but it was still a burden for one person to make all one hundred calls. And even if someone set out to do this, it might take quite a while to get to the people at the end of the list, by which time they may have already left home for school. Having a single person make all the calls is both inefficient and burdensome.
Ideally, one person would set off a chain reaction so that everyone could be reached as quickly as possible and with the least burden on any particular individual. One option is to create a list and have the person at the top of the list call the next person, the second person call the third, and so on until everyone gets the message, as in a bucket brigade. This would distribute the burden evenly, but it would still take a really long time for the hundredth person to be reached. Moreover, if someone in the sequence was not home when called, everyone later in the list would be left in the dark.
An alternative pattern of connections is a telephone tree. The first person calls two people, who each call two people, and so on until everyone is contacted. Unlike the bucket brigade, the telephone tree is designed to spread information to many people simultaneously, creating a cascade. The workload is distributed evenly among all group members, and the problem caused by one person not being home is limited. Moreover, with a single call, one person can set off a chain of events that could influence hundreds or thousands of other people—just as the person who donated the heart that was transplanted into John Lavis prompted another donation that saved eight more lives. The telephone tree also vastly reduces the number of steps it takes for information to flow among people in the group, minimizing the chance that the message will be degraded. This particular network structure thus helps to both amplify and preserve the message. In fact, within a few decades of the widespread deployment of home-based phones in the United States, telephone trees were used for all sorts of purposes. An article in the Los Angeles Times from 1957, for example, describes the use of a phone tree to mobilize amateur astronomers, as part of the “Moonwatch System” of the Smithsonian Astrophysical Observatory, to track American and Russian satellites.8
Alas, this same network structure also allows a single swindler to cheat thousands of people. In Ponzi schemes, money flows “up” a structure like a telephone tree. As new people are added to the network, they send money to the people “above” them and then new members are recruited “below” them to provide more money. As time passes, money is collected from more and more people. In what might be the biggest Ponzi scheme of all time, federal investigators discovered in 2008 that during the previous thirty years Bernie Madoff had swindled $50 billion from thousands of investors. Like the Corsican vendetta network we described earlier, Madoff’s investment network is the kind most of us would like to avoid.
The four different types of networks we have considered so far are shown in the illustration. First is a group of one hundred people (each represented by a circle, or node) among whom there are no ties. Next is a bucket brigade. Here, in addition to the one hundred people, there are a total of ninety-nine ties between the members of the group; every person (except the first and last) is connected to two other people by a mutual tie (meaning that full and empty buckets pass in both directions). In the telephone tree, there are one hundred people and again ninety-nine ties. But here, everyone, with the exception of the first and last people in the tree, is connected to three other people, with one inbound tie (the person they get the call from) and two outbound ties (the people they make calls to). There are no mutual ties; the flow of information is directional and so are the ties between people. In a company of one hundred soldiers, each member of each squad knows every other member of the squad very well; and each person has exactly nine ties. Here, there are one hundred people and 450 ties connecting them. (The reason there are not nine hundred ties is that each tie counts once for the two people it connects.) In the drawing, we imagine that there are no ties between squads or, at least, that the ties within squads are much tighter than the ties between squads. This is clearly an oversimplification, but it illustrates still another point about communities in social networks. A network community can be defined as a group of people who are much more connected to one another than they are to other groups of connected people found in other parts of the network. The communities are defined by structural connections, not necessarily by any particular shared traits.
Four different ways to connect one hundred people. Each circle (“node”) represents a person, and each line (“tie”) a relationship between two people. Lines with arrows indicate a directed relationship; in the telephone tree, one person calls another. Otherwise, ties are mutual: in the bucket brigade, full and empty buckets travel in both directions; in military squads, the connections between the soldiers are all two-way.
In a very basic sense, then, a social network is an organized set of people that consists of two kinds of elements: human beings and the connections between them. Unlike the bucket brigade, telephone tree, and military company, however, the organization of natural social networks is typically not imposed from the top. Real, everyday social networks evolve organically from the natural tendency of each person to seek out and make many or few friends, to have large or small families, to work in personable or anonymous workplaces.
For example, in the next illustration, we show a network of 105 students in a single dormitory at an American university and the friendship ties between them. On average, each student is connected to six other close friends, but some students have only one friend, and others have many. Moreover, some students are more embedded than others, meaning they have more connections to other people in the network via friends or friends of friends. In fact, network visualization software is designed to place those who are more interconnected in the center and those who are less interconnected at the periphery, helping us to see each person’s location in the network. When your friends and family become better connected, it increases your level of connection to the whole social network. We say it makes you more central because having better-connected friends literally moves you away from the edges and toward the center of a social network. And we can measure your centrality by counting not just the number of your friends and other contacts but also by counting your friends’ friends, and their friends, and so on. Unlike the bucket brigade where everyone feels his position to be the same (“there’s a guy on my left passing me buckets and a guy on my right to whom I give them—it doesn’t matter where in the line I am”), here, people are located in distinctly different kinds of places within the network.
In this natural network of close friendships among 105 college students living in the same dormitory, each circle represents a student, and each line a mutual friendship. Even though A and B both have four friends, A’s
