Reach out and touch someone, AT&T famously encouraged. Even way back in 1979, when the telecom firm launched its campaign, the world had grown increasingly interconnected. Today, networks have proliferated, making it easier to link with others a world away.
And that world has become smaller, a point of departure for new research on network dynamics by Kellogg School of Management assistant professor of managerial and decision sciences Brian W. Rogers and Stanford University colleague professor Matthew O. Jackson.
The scholars have presented a dynamic model of network formation illustrating how, through both random and network-based meetings, these connections arise among “nodes” in the system.
The research—Meeting Strangers and Friends of Friends: How Random Are Social Networks?—was published in the June issue of The American Economic Review. There are many social networks, Rogers says, including personal friendships, email correspondence, Web chat rooms and scientific collaborations.“Though they come from really different settings, the structures of these networks are found empirically to have quite a lot in common,” says Rogers, whose expertise includes game theory and microeconomics. But, until recently, it has been unclear why an online network and an academic collaboration should share many of the same structural features.
“We wanted to write a model that can be seen as a reasonable description of how networks form in all these different applications,” says Rogers. In so doing, the researchers revealed the network characteristics common to those applications.
The study analysed six data sets of different networks and how those were formed. These include all the pages on a large college website, a group of researchers in economics and the papers that they authored together, a network of truck drivers who made ham-radio calls to each other, friendships among prison inmates, and romantic relationships among a sample of high-school students.
The analysis shed new light on what has been termed the “small-world effect”, a concept introduced by Hungarian author Frigyes Karinthy in 1929. The idea was later developed and demonstrated experimentally by social psychologist Stanley Milgram in 1967, when he tracked chains of acquaintances in the US to reveal that a surprisingly small number of connections linked people —even those seemingly far apart socially. Rogers and Jackson also used the small worlds concept to consider their data.
“Small worlds” may be familiar to some people, says Rogers, especially in the concept’s formulation as “six degrees of separation”. He says: “The most well-known aspect of the framework is that if you pick two random strangers, there is a good chance that a short network path connects them.” In other words, these people frequently will have a common friend.
A second characteristic of this model involves clustering, or the tendency for connections to exist among those sharing a mutual friend. “If I have two friends, then they’re very likely to themselves be friends of each other, compared to the case where they didn’t have me as a common friend,” Rogers says.
In the model developed by Rogers and Jackson, individuals enter a network sequentially, forming relationships in tandem with other people in two ways: First, some links are created independently—such as when a person meets a neighbour upon moving to a new home. “When you meet these people, there’s some probability that you’re compatible and you want to have a friendship, in which case you form a connection,” Rogers says.
Upon forming these random friendships, people are often introduced to their local network. As in the first scenario, “There is some chance that the people will feel mutually compatible and they are likely to form a connection.” This process is similar to how Web pages are linked together, Rogers notes: Starting at one website, a person discovers other pages by tracing hyperlinks that lead to other pages that may be of interest.
The ideas presented in this paper are related to results that Rogers and Jackson published inThe B.E. Journal of Theoretical Economicsin February. That study examined diffusion across similar networks, indicating, for example, how a disease or rumour might spread and whether it will persist.
“In the last 15 years, this subject has gone from being almost non-existent from an economist’s perspective to being one of the hottest topics,” says Rogers. He notes that Jackson, an economist and former Kellogg School professor, has been a leader in this area of study and has had a tremendous influence on Rogers’ own research. The two met and collaborated at the California Institute of Technology where Rogers earned his social sciences doctorate before joining Kellogg in 2006.
One area where the economic conceptions of networks prove important is in criminology. Rogers says that recent research makes interesting predictions about how crime rates depend on the structure of social networks. “The returns to committing crimes depend, for instance, on whether or not your friends are also criminals,” he says. But other factors, such as the network’s overall level of crime, also matter, since this activity can influence the level of police monitoring, which in turn can curtail the illegal actions.
Another example of the application of this research is found in consideration of segregation and employment, or socioeconomic status dynamics. “There are models that explain how, if society is segregated, some segments of the population can remain stuck at low wage/employment socioeconomic status levels for a long time even in the absence of discrimination,” says Rogers.
Linking the facts and figures of such models to flesh-and-blood concerns helps increase the utility of economics to explain critical social dynamics.
“There are situations that economists try to explain or model and, for the most part, they have done that ignoring the social structure in which information transmissions are taking place,” says Rogers. “You can wind up missing a lot of important facts that you could characterize by using networks.”
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