Applying Physics to Complex Social Systems

Michelle Girvan, the Ginny and Robert Loughlin Founders’ Circle Member in the School of Social Science during the 2008–09 academic year, is one of many physicists who have been drawn in recent years to study complex systems beyond the purely physical. Using graph theory, statistical physics, algorithms, and nonlinear dynamics, these researchers can describe phenomena such as the connection of Internet sites and the spread of rumors and disease in mathematical terms, yielding some surprising results.

While at the Institute, Girvan, an Assistant Professor in the Department of Physics at the University of Maryland, has been examining how individuals’ social networks and opinions develop in concert, as they seek to be like their neighbors and connect to other people like themselves, while still forming some opinions based on independent reflection.

“We see that there is a tipping point in the parameters of this model, in which the system goes from one that is built from closely knit groups between which there are only looser connections to one in which there is only one group with a single opinion,” Girvan explains.

Girvan is also looking for algorithms that will identify overlapping community structures in networks, helping to explain, for example, how business, social, and family ties interact. If one of these communities is disrupted, what will happen to the others? This is a question Girvan began looking into some years ago, at one point collaborating with a group of researchers studying primates in a project that demonstrates how mathematical modeling can reveal social forces.

In primate societies, a few older males often serve as a sort of police, intervening in conflicts when they arise and preventing others by their mere presence. Following a typical method of zoological observation, researchers removed these policing individuals from a group of captive pigtailed macaques, a type of monkey native to Southeast Asia, and observed the results. But before the observations were made, Girvan added another step: she constructed a topological model of what could be expected when these males were removed based on the network structure of their relationships, in which the policing males serve as nodes in a web of connections.

In a paper published in Nature in January 2006, the team reported the results. Simple observation of the macaques revealed the disruptiveness of removing the policing males. In their absence, the other macaques played with, groomed, and sat with far fewer partners than they did when the dominant males were present. But the topological model projected a higher level of ­disruption—­if equally important nodes were removed from a physical structure, the collapse would have been more significant. The comparison revealed that the remaining macaques were in fact compensating for the absence of the policing males to some degree, restructuring some of their relationships to withstand the removal of these central figures. Such dynamics can now be investigated further, both by primatologists and by ­complex-­network theorists like Girvan. ■