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 every- one could be reached as quickly as possible and with the least bur- den 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, cre- ating 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 , for example, 10 i-xiv r4sr.
As time passes, money is collected from more and more people. 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 hun- dred people and 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 11 i-xiv r4sr. Lines with arrows indicate a directed relation- ship; 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 sol- diers are all two-way.
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 12 i-xiv r4sr.
The com- munities are defined by structural connections, not necessarily by any particular shared traits.
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, every- day 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 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. 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.
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. 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 14 i-xiv r4sr. 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 com- ponents 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 fun- damental 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 topol- ogy by putting the most tangled buttons in the center and the least connected ones on the edges.
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 struc- ture, 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. First, there is con- nection, 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 inter- est. 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.
Birds of a feather flock together. But we also choose the structure of our networks in three impor- tant 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 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 struc- tures 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 17 i-xiv r4sr.
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 impor- tant 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 aver- age 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. 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 rela- tionships 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 probabil- ity 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, fam- ily, coworkers, and neighbors, but these people are in turn connected to their friends, family, coworkers, and neighbors, and so on end- lessly 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. A famous example at least among social scientists was described in a paper first drafted in the s by two early figures in the study of social networks, Ithiel de Sola Pool and Manfred Kochen.
He was——from Shanghai. A person who has no friends has a very different life than one who has many. One study of hundreds of thousands of Norwegian military con- scripts provides a simple example of how the mere number of social contacts here, siblings can affect you.
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. 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 par- ents, but her life is different depending on whether or not they are connected. And how many contacts your friends and family have is also rel- evant.
When the people you are connected to become better con- nected, 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 fig- ure 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.
What actually flows across the connections is also cru- cial. 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 21 i-xiv r4sr. 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 mani- cured lawns.
And this simple tendency for one person to influence another has tremendous consequences when we look beyond our immediate connections. 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. It is easy to think about hyperdyadic effects when the network is 22 i-xiv r4sr. But how on earth can they be understood in a natural social network such as the col- lege 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. 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.
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