[CAnet - news] "Six Degrees of Separation" Theory Explained in New Algorithm

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[Thanks to Harvey Newman for this pointer.  This theory has interesting
implications for networking -- BSA]



 http://www.umass.edu/newsoffice/newsreleases/articles/20618.php

"Six Degrees of Separation" Theory Explained in New Algorithm by UMass
Amherst Researchers

Sept. 6, 2005

Contact:        Rachel Ehrenberg <mailto:[email protected]>
413/545-0444

AMHERST, Mass. - University of Massachusetts Amherst researchers have
invented a new algorithm that solves a network-searching conundrum that has
puzzled computer scientists and sociologists for years.

The scientists created an algorithm that helps explain the sociological
findings that led to the theory of "six degrees of separation," and could
have broad implications for how networks are navigated, from improving
emergency response systems to preventing the spread of computer viruses.

Dubbed expected-value navigation, the algorithm describes an efficient way
of searching a particular class of networks and was presented by doctoral
student Ozgur S,ims,ek, and David Jensen, professor of computer science, at
the 19th International Joint Conference on Artificial Intelligence in
Edinburgh, Scotland.

The algorithm is applicable to a number of networks say the researchers.
Ad-hoc wireless networks, peer-to-peer file sharing networks and the World
Wide Web are all systems that could benefit from more efficient
message-passing. The algorithm could work especially well with dynamic
systems such as ad-hoc wireless networks where the structure may change so
quickly that a centralized hub becomes obsolete.

The work was inspired by research pioneered in the late 1960s that focused
on navigating social networks, explains S,ims,ek. In a now famous study by
psychologists Milgram and Travers, individuals in Boston and Omaha, Neb.,
were asked to deliver a letter to a target person in Boston, but via an
unconventional route: the message had to be passed through a chain of
acquaintances. The people starting the chain had some basic information
about the target individual-including name, age and occupation-and were
asked to forward the letter to someone they knew on a first-name basis in an
effort to deliver it through as few intermediaries as possible. Of the
letters that reached the target, the median number of people in the
message-passing chain was a mere six.

"What came out of that study was that we are all connected," says S,ims,ek.
But the findings also raised a number of questions about how we are
connected, she says. What are the properties of these networks and how do
people efficiently navigate them?

The social network exploited by Travers and Milgram isn't a straightforward,
evenly patterned web. For one thing, network topology is only known
locally-individuals starting with the letter did not know the target
individual-and the network is decentralized-it didn't use a formal hub such
as the post office. If navigating such a network is to succeed-and tasks
such as searching peer-to-peer file sharing systems or the navigating the
Web by jumping from link to link do just that-there must be parts of the
underlying structure that successfully guide the search, argue Jensen and
S,ims,ek.

Participants in the Travers and Milgram study who efficiently sent the
message probably acted intuitively by combining two human traits that apply
to computerized network-searching as well, say the researchers. People tend
to associate with people who are like themselves, and some individuals are
more gregarious than others. "Searching" using both of these factors, one
can efficiently get to a target even when little is known about the
network's structure.

The tendency of like to associate with like, or homophily, means that
attributes of a node-an individual in the Travers and Milgram study-tend to
be correlated. Bostonians often know other Bostonians, and the same holds
true for qualities such as age or occupation. The second important
characteristic of these networks is that some people have many more
acquaintances than others. This "degree disparity" leads to some individuals
acting as hubs.

Taking these factors into account simultaneously results in a searching
algorithm that gets messages to the target by passing it to gregarious
individuals who are most like the target. Or in the language of
network-searching, it favors nodes that maximize the probability of linking
directly to the target, which is a function of both degree and homophily,
say the scientists.

Previous research had explored these aspects separately, but S,ims,ek and
Jensen are the first to step back and incorporate both these qualities into
one broadly applicable algorithm with a strong basis in probability theory.
And the combination yields a powerful punch. It is remarkably efficient at
finding the short paths between nodes without knowing the central network's
structure, say the researchers

"In this case, one plus one is more than two," says S,ims,ek.





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