Physics meets Sociometry: Determining Dynamics of Friends and Enemies

Name: J.Elz-Fianda, Dr.med., D-86720 Noerdlingen, GERMANY
email: jochenmabuse@web.de
_http://www.physorg.com/news178954961.html_

*(PhysOrg.com) -- Sometimes friends can become enemies and enemies
become friends, and it's difficult to understand exactly how or why the
changes took place.
A new study shows that when the shifting of alliances and rivalries is
interpreted using principles from social psychology, the overall
behavior can be modeled as arising from an energy minimization process.
The work is part of a growing line of research that uses tools from
physics to analyze complex social systems.*

In their study, Seth Marvel, Steven Strogatz, and Jon Kleinberg from
Cornell University have used theories from social psychology to classify
certain configurations of friends <http://www.physorg.com/tags/friends/>
and enemies as being more stable than others. They show that these
configurations can be represented by an energy landscape, in which the
overall social stress <http://www.physorg.com/tags/social+stress/>
corresponds to a kind of energy that relaxes as relationships shift
between friends and enemies.

In their model, the researchers used plus signs to represent friendships
between two individuals, and minus signs when two individuals were enemies.
Some configurations in a group were considered balanced, while others
were unbalanced. For example, in a balanced configuration, the enemy of
your enemy should be your friend, and the friend of your enemy should be
your enemy.
In the scientists' model, these balanced configurations require less
energy to maintain, and are the global minima in the energy landscape.
The configurations of lowest possible energy are those in which all
pairs in the network are friends, or in which the network is divided
into two "rival factions": two groups of mutual friends who are
antagonistic toward each other.

While this description of the lowest-energy configurations has been
studied in previous work, the researchers found that the overall energy
landscape is more complex than previously thought. Specifically, they
found that "jammed states," or local minima, occur when a configuration
is trapped between adjacent configurations of higher energy, prohibiting
it from moving toward the lowest energy state (a balanced configuration).
When investigating the structure of these jammed states, the researchers
found that these states form more often at lower energies, and
higher-energy jammed states are structurally more complex than
lower-energy jammed states.

"Earlier work by Antal, Krapivsky, and Redner had shown that jammed
states could exist, and so our interest was in developing a more
complete picture of the possible energy levels and structures of these
jammed states," Kleinberg said said to /PhysOrg.com/. "We find that
jammed states can exist at surprisingly high energies, and that the
pattern of friend/enemy relationships within a jammed state has an
inherent complexity that increases as we move higher up the energy
landscape."

These results provide a first look at how social networks can be viewed
as energy landscapes that are driven by minimizing social stress (or, by
the same token, increasing consistency in relationships). While this
study reveals insight into the landscape's local and global minima, in
the future the researchers hope to better understand the large-scale
structure. By doing so, they could possibly find pathways leading from
the most entrenched conflicts toward states of reconciliation.

"Our model is a theoretical one; it explores the consequences that
follow logically from a few simple principles in social psychology
<http://www.physorg.com/tags/social+psychology/>, and it shows that
these consequences can be surprisingly complex," Kleinberg said.
"We think it could help provide a guiding framework for reasoning about
real-life social networks in which there is both friendship and
conflict, and in particular it could provide a useful perspective for
subsequent empirical studies aimed at interpreting the patterns of
friend and enemy relations that one finds in real data."

_More information:_ Seth A. Marvel, Steven H. Strogatz, and Jon M.
Kleinberg. "Energy Landscape of Social Balance." /Physical Review
Letters/, 103, 198701 (2009).

You can read the preprint of this study here
_http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.2893v2.pdf_
<http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.2893v2.pdf>