So far we have discussed very basic mathematical methods in analyzing social networks, using basic graph theory and other mathematics traditionally used in network study. This paper* presents an analysis of social networks using a strictly physical analogy—that is, applying laws of kinematics within a closed set of people to show that clear social networks emerge. What is surprising, however, is that the model that comes out describes characteristics of normal social networks that we see all the time.

The model uses particles to represent individuals in a network, and collisions between particles to measure interactions between individuals. Particles react to collisions by changing speed and direction which then could result in more collisions, just as interactions between people change according to previous interactions. Surprisingly, however, is that given a constant number of particles, the system will eventually reach a “quasistationary state,” a sort of equilibrium that approximates many features of social networks. The authors show that in this state, properties such as shortest path length, clustering coefficient (how clustered some groups are) and degree distribution are similar to a social network measured by conventional means (the authors took data about friendships in comparison). Communities arise just as in social networks via this model.

The authors extended this model for specific applications: for example, the spread of HIV could be real-life circumstances just by adding indication of sexual contact to the model. The implications of this model are that statistically, random collisions, if described accurately, are similar to the random social “collisions” present within a social network. While particle motion does not exactly model human interactions, given a statistically significant sample, similar properties do emerge. This model thus gives a natural instance of human social networks, one that does not involve polling a large group of people to get results. If this model can be applied to different circumstances, social network analysis may become simpler to achieve since empirical data can be found without polling large samples of people.

*Gonzalez, Marta C., Lind, Pedro G. and Herrmann, Hans J. System of Mobile Agents to Model Social Networks. Physical Review Letters. 96, 088702 (2006).