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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 four friends are more likely to know one another (there are ties between them), whereas none of B’s friends know each other. A has greater transitivity than B. Also, even though C and D both have six friends, they have very different locations in the social network. C is much more central, and D is more peripheral; C’s friends have many friends themselves, whereas D’s friends tend to have few or no friends.

A network’s shape, also known as its structure or topology, is a basic property of the network. While the shape can be visualized, or represented, in different ways, the actual pattern of connections that determines the shape remains the same regardless of how the network is visualized. Imagine a set of five hundred buttons strewn on the floor. And imagine that there are two thousand strings we can use to connect the buttons. Next, imagine that we randomly select two buttons and connect them with a string, knotting each button at the end. Then we repeat this procedure, connecting random pairs of buttons one after another, until all the strings are used up. In the end, some buttons will have many strings attached to them, and others, by chance, will never have been picked and so will not be connected to another button. Perhaps some groups of buttons will be connected to each other but separated from other groups. These groups—even those that consist of a single unconnected button—are called components of the network; when we illustrate networks, we frequently represent only the largest component (in this case, the one with the most buttons).

If we were to select one button from one component and pick it up off the floor, all other buttons attached to it, directly or indirectly, would also be lifted into the air. And if we were to drop this mass of buttons onto another spot on the floor, it would look different than it did when we first picked it up. But the topology—which is a fundamental and intrinsic property of the network of buttons—would be exactly the same, no matter how many times we picked up and dropped the mass of connected buttons. Each button has the same relational position to other particular buttons that it had before; its location in the network has not changed. Visualization software tries to show this in two dimensions and to reveal the underlying topology by putting the most tangled buttons in the center and the least connected ones on the edges. It’s as if you were trying to untangle a gnarled set of Christmas-tree lights, and there were tendrils of the gnarled mess that you could pull out, and also a thicket of inter-knotted lights that remained in the center no matter how often you turned the tangle over on the floor.

For numerous reasons we will explore, people come to occupy particular spots in the naturally occurring and continuously evolving social networks that surround us. Organic networks have a structure, complexity, function, spontaneity, and sheer beauty not found in organized networks, and their existence provokes questions about how they arise, what rules they obey, and what purpose they serve.

Rules of Life in the Network

There are two fundamental aspects of social networks, whether they are as simple as a bucket brigade or as complex as a large multigenerational family, a college dormitory, an entire community, or the worldwide network that links us all. First, there is connection, which has to do with who is connected to whom. When a group is constituted as a network, there is a particular pattern of ties that connects the people involved, the topology. Moreover, ties are complicated. They can be ephemeral or lifelong; they can be casual or intense; they can be personal or anonymous. How we construct or visualize a network depends on how we define the ties of interest. Most analyses emphasize ties to family, friends, coworkers, and neighbors. But there are all sorts of social ties and, thus, all sorts of social networks. In fact, when things such as sexually transmitted diseases or dollar bills flow through a network, this flow itself can define the ties and hence the structure of a particular set of network connections.

Second, there is contagion, which pertains to what, if anything, flows across the ties. It could be buckets of water, of course, but it also could be germs, money, violence, fashions, kidneys, happiness, or obesity. Each of these flows might behave according to its own rules. For example, fire cannot be transported in buckets toward the river; germs cannot affect someone who is immune; and obesity, which we will discuss in chapter 4, tends to spread faster between people of the same sex.

Understanding why social networks exist and how they work requires that we understand certain rules regarding connection and contagion—the structure and function—of social networks. These principles explain how ties can cause the whole to be greater than the sum of the parts.

RULE 1: WE SHAPE OUR NETWORK

Humans deliberately make and remake their social networks all the time. The primary example of this is homophily, the conscious or unconscious tendency to associate with people who resemble us (the word literally means “love of being alike”). Whether it’s Hells Angels or Jehovah’s Witnesses, drug addicts or coffee drinkers, Democrats or Republicans, stamp collectors or bungee jumpers, the truth is that we seek out those people who share our interests, histories, and dreams. Birds of a feather flock together.

But we also choose the structure of our networks in three important ways. First, we decide how many people we are connected to. Do you want one partner for a game of checkers or many partners for a game of hide-and-seek? Do you want to stay in touch with your crazy uncle? Do you want to get married, or would you rather play the field? Second, we influence how densely interconnected our friends and family are. Should you seat the groom’s college roommate next to your bridesmaid at the wedding? Should you throw a party so all your friends can meet each other? Should you introduce your business partners? And third, we control how central we are to the social network. Are you the life of the party, mingling with everyone at the center of the room, or do you stay on the sidelines?

Diversity in these choices yields an astonishing variety of structures for the whole network in which we come to be embedded. And it is diversity in these choices—a diversity that has both social and genetic origins as we will see in chapter 7—that places each of us in a unique location in our own social network. Of course, sometimes these structural features are not a matter of choice; we may live in places that are more or less conducive to friendship, or we may be born into large or small families. But even when these social-network structures are thrust upon us, they still rule our lives.

We actually know quite a bit about how people vary in terms of how many friends and social contacts they have and in how interconnected they are. Yet, identifying who a person’s social contacts are can be a tricky business since people have many interactions of varying intensities with all sorts of people. While a person may know a few hundred people by sight and name, he will typically be truly close to only a few. One way social scientists identify such close individuals is to ask questions like, who do you discuss important matters with? Or, who do you spend your free time with? When answering such questions, people will identify a heterogeneous mix of friends, relatives, coworkers, schoolmates, neighbors, and others.

We recently put these questions to a sample of more than three thousand randomly chosen Americans. And we found that the average American has just four close social contacts, with most having between two and six. Sadly, 12 percent of Americans listed no one with whom they could discuss important matters or spend free time. At the other extreme, 5 percent of Americans had eight such people. About half of the people listed as members of Americans’ intimate groups were said to be friends, but the other half included a wide variety of different kinds of relationships, including spouses, partners, parents, siblings, children, coworkers, fellow members of clubs, neighbors, and professional advisers and consultants. Sociologist Peter Marsden has called this group of people that we all have a “core discussion network.” In a national sample of 1,531 Americans studied in the 1980s, he found that core-discussion-network size decreases as we age, that there is no overall difference between men and women in core-network size, and that those with a college degree have core networks that are nearly twice as large as those who did not finish high school.⁹

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 to spread from person to person to person, beyond an individual’s direct social ties. Corto’s brother lost his life because of such spread.

It is easy to think about hyperdyadic effects when the network is a straight line—(“that guy three people down the line better pass the bucket, or we’re all going to be in big trouble”). But how on earth can they be understood in a natural social network such as the college students in the illustration on page 14, or complex networks of thousands of people with all kinds of crosscutting paths stretching far beyond the social horizon (as we will consider later)? To decipher what is going on, we need two kinds of information. First, we must look beyond simple, sequential dyads: we need to know about individuals and their friends, their friends’ friends, their friends’ friends’ friends, and so on. And we can only get this information by observing the whole network at once. It has just recently become possible to do this on a large scale. Second, if we want to observe how things flow from person to person to person, then we need information about the ties and the people they connect at more than one point in time, otherwise we have no hope of understanding the dynamic properties of the network. It would be like trying to learn the rules of an unfamiliar sport by looking at a single snapshot of a game.

We will consider many examples and varieties of hyperdyadic spread, but we can set the stage with a simple one. The usual way we think about contagion is that if one person has something and comes into contact with another person, that contact is enough for the second person to get it. You can become infected with a germ (the most straightforward example) or with a piece of gossip or information (a less obvious example). Once you get infected by a single person, additional contact with others is generally redundant. For example, if you have been told accurately that stock XYZ closed at $50, another person telling you the same thing does not add much. And you can pass this information on to someone else all by yourself.

But some things—like norms and behaviors—might not spread this way. They might require a more complex process that involves reinforcement by multiple social contacts. If so, then a network arranged as a simple line, like a bucket brigade, might not support transmission of more complicated phenomena. If we wanted to get people to quit smoking, we would not arrange them in a line and get the first one to quit and tell him to pass it on. Rather, we would surround a smoker with multiple nonsmokers, perhaps in a squad.

Psychologist Stanley Milgram’s famous sidewalk experiment illustrates the importance of reinforcement from multiple people. ¹² On two cold winter afternoons in New York City in 1968, Milgram observed the behavior of 1,424 pedestrians as they walked along a fifty-foot length of street. He positioned “stimulus crowds,” ranging in size from one to fifteen research assistants, on the sidewalk. On cue, these artificial crowds would stop and look up at a window on the sixth floor of a nearby building for precisely one minute. There was nothing interesting in the window, just another guy working for Milgram. The results were filmed, and assistants later counted the number of people who stopped or looked where the stimulus crowd was looking. While 4 percent of the pedestrians stopped alongside a “crowd” composed of a single individual looking up, 40 percent stopped when there were fifteen people in the stimulus crowd. Evidently, the decisions of passersby to copy a behavior were influenced by the size of the crowd exhibiting it.

An even larger percentage of pedestrians copied the behavior incompletely: they looked up in the direction of the stimulus crowd’s gaze but did not stop. While one person influenced 42 percent of passersby to look up, 86 percent of the passersby looked up if fifteen people were looking up. More interesting than this difference, however, was that a stimulus crowd of five people was able to induce almost as many passersby to look up as fifteen people did. That is, in this setting, crowds larger than five did not have much more of an effect on the actions of passing individuals.