Faculty Research: Brian Rogers, MEDS
is a small world after all
research by MEDS Professor Brian Rogers shows why the ties
out and touch someone, AT&T famously encouraged. Even
way back in 1979, when the telecommunications company launched
its campaign, the world had grown increasingly interconnected.
Today, networks have proliferated, making it even easier to
link with others a world away.
that world has become smaller, a point of departure for new
research on network dynamics by 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.
research — "Meeting Strangers and Friends of Friends:
How Random Are Social Networks?" — is published
in the June issue of The American Economic Review.
are many social networks, Rogers says, including personal
friendships, e-mail correspondences, Web chat rooms and boards,
and scientific collaborations, to name a few. "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.
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.
study analyzed six data sets of different networks and how
those formed. These include all the pages on a large college
Web site; 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
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 U.S. to reveal
that a surprisingly small number of connections ("nodes")
linked people — even those seemingly far apart socially.
The small worlds concept is also a lens through which Rogers
and Jackson considered their data.
worlds" may be familiar to some people, says Rogers,
especially in its formulation as "six degrees of separation."
The Kellogg professor 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.
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,"
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 neighbor upon moving
to a new home.
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.
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 Web site, a person discovers other pages by
tracing hyperlinks that lead to other pages that may be of
ideas presented in this paper are related to results that
Rogers and Jackson published in the BE Journal of Theoretical
Economics in February. That study examined diffusion across
similar networks, indicating, for example, how a disease or
rumor might spread into a population and whether it will persist.
the last 15 years [this subject] has gone from being almost
nonexistent 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.
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.
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,"
the facts and figures of such models to flesh-and-blood concerns
helps increase the utility of economics to explain critical
are situations that economists try to explain or model, and
for the most part they have done that ignoring the social
structure in which transactions or information transmissions
are taking place," says Rogers. "You can wind up
missing a lot of important facts that you could characterize
by using networks."