Next, in our own work, we asked the respondents to tell us how interconnected their social contacts were to each other. So if a person said that Tom, Dick, Harry, and Sue were his friends, we asked him if Tom knew Dick, if Tom knew Harry, if Tom knew Sue, if Dick knew Harry, and so on. We then used these answers to calculate the probability that any two of a person’s friends were also friends with each other. This probability is an important property that we use to measure how tightly interwoven a network is.
If you know Alexi, and Alexi knows Lucas, and Lucas knows you, we say this relationship is transitive—the three people involved form a triangle. Some people live in the thick of many transitive relationships (like person A in the illustration on page 14), while others have friends who do not know each other (like person B). Those with high transitivity are usually deeply embedded within a single group, while those with low transitivity tend to make contact with people from several different groups who do not know one another, making them more likely to act as a bridge between different groups. Overall, we found that if you are a typical American, the probability that any two of your social contacts know each other is about 52 percent.
Although these measures characterize the networks we can see, they also tell us something about the networks we cannot see. In the vast fabric of humanity, each person is connected to his friends, family, coworkers, and neighbors, but these people are in turn connected to their friends, family, coworkers, and neighbors, and so on endlessly into the distance, until everyone on earth is connected (pretty much) to everyone else, one way or another. So whereas we think of our own network as having a more limited social and geographic reach, the networks that surround each of us are actually very widely interconnected.
It is this structural feature of networks that underlies the common expression “it’s a small world.” It is often possible, through a few connections from person to person, for an individual to discover a connection to someone else. A famous example (at least among social scientists) was described in a paper first drafted in the 1950s by two early figures in the study of social networks, Ithiel de Sola Pool and Manfred Kochen. One of the authors overheard a patient in a hospital in a small town in Illinois say to a Chinese patient in the adjoining bed: “You know, I’ve only known one Chinese before in my life. He was….from Shanghai.” Whereupon the response came back, “Why, that’s my uncle.”10 In fact, the authors did not tell us his name, perhaps because they were worried that the reader, in a further illustration of the small-world effect, would know him.
RULE 2: OUR NETWORK SHAPES US
Our place in the network affects us in turn. A person who has no friends has a very different life than one who has many. For example, we will see in chapter 4 that having an extra friend may create all kinds of benefits for your health, even if this other person doesn’t actually do anything in particular for you.
One study of hundreds of thousands of Norwegian military conscripts provides a simple example of how the mere number of social contacts (here, siblings) can affect you.11 It has been known for some time that first-born children score a few points higher in terms of intelligence than second-born children, who in turn score a bit higher than third-born children. One of the outstanding questions in this area of investigation, however, has been whether these differences are due to biological factors fixed at birth or to social factors that come later. The study of Norwegian soldiers showed that simple features of social networks, such as family size and structure, are responsible for the differences. If you are a second-born son whose older sibling died while you were a child, your IQ increases and resembles the IQ of a first-born child. If you are a third-born child and one of your older siblings died, your IQ resembles that of a second-born child; and if both of your older siblings died, then your IQ resembles that of a first-born child.
Whether your friends and other social contacts are friends with one another is also crucial to your experience of life. Transitivity can affect everything from whether you find a sexual partner to whether you commit suicide. The effect of transitivity is easily appreciated by the example of how divorce affects a child. If a child’s parents are married (connected) then they probably talk to each other, but if they get divorced (disconnected) they probably do not. Divorce means that communication often has to pass through the child (“Tell your father not to bother picking you up next Saturday!”), and it is much harder to coordinate raising the child (“You mean your mother bought you ice cream too?”). What is remarkable is that even though the child is still deeply connected to both parents, her relationship with each of them changes as a consequence of the divorce. Yet these changes result from the loss of a connection between the parents—a connection the child has little to do with. The child still has two parents, but her life is different depending on whether or not they are connected.
And how many contacts your friends and family have is also relevant. When the people you are connected to become better connected, it reduces the number of hops you have to take from person to person to reach everyone else in the network. You become more central. Being more central makes you more susceptible to whatever is flowing within the network. For example, person C in the figure on page 14 is more central than person D. Ask yourself which person you would rather be if a hot piece of gossip were spreading; you should be person C. Now ask yourself which person you would rather be if a deadly germ were spreading in the network; you should be person D. And this is the case even though persons C and D each have the same number of social ties: they are each directly connected to just six people. In later chapters, we will show how your centrality affects everything from how much money you make to whether you will be happy.
RULE 3: OUR FRIENDS AFFECT US
The mere shape of the network around us is not all that matters, of course. What actually flows across the connections is also crucial. A bucket brigade is formed not to make a pretty line for you to look at while your house is burning but so that people can pass water to each other to douse the flames. And social networks are not just for water—they transport all kinds of things from one person to another.
As we will discuss in chapter 2, one fundamental determinant of flow is the tendency of human beings to influence and copy one another. People typically have many direct ties to a wide variety of people, including parents and children, brothers and sisters, spouses (and nice ex-spouses), bosses and coworkers, and neighbors and friends. And each and every one of these ties offers opportunities to influence and be influenced. Students with studious roommates become more studious. Diners sitting next to heavy eaters eat more food. Homeowners with neighbors who garden wind up with manicured lawns. And this simple tendency for one person to influence another has tremendous consequences when we look beyond our immediate connections.
RULE 4: OUR FRIENDS’ FRIENDS’ FRIENDS AFFECT US
It turns out that people do not copy only their friends. They also copy their friends’ friends, and their friends’ friends’ friends. In the children’s game telephone, a message is passed along a line by each child whispering into the next child’s ear. The message each child receives contains all the errors introduced by the child sharing it as well as those introduced by prior children to whom the child is not directly connected. In this way, children can come to copy others to whom they are not directly tied. Similarly, every parent warns children not to put money in their mouths: the money, we think, contains germs from numerous people whose hands it has passed through, and not just from the most recent pair of hands. Analogously, our friends and family can influence us to do things, like gain weight or show up at the polls. But their friends and family can influence us too. This is an illustration of hyperdyadic spread, or the tendency of effects
