William and Mary

A model of structrual balance in social networks

Topic description:  In a recent article by Marvel, a differential equation model of structural balance in social psychology was proposed. It was shown that the group will split into two factions of friends in a finite time. However the proposed differential equation has a finite-time blowup structure, and there are terms of self-approval or self-confidence in the equation which may not be the best possible choice.

Seth A. Marvel, Jon Kleinberg, Robert D. Kleinberg, and Steven H. Strogatz, Continuous-time model of structural balance. Proc Natl Acad Sci U S A. 2011 February 1; 108(5): 1771–1776.

Research opportunities:  We will modify the model in the above paper: (i) remove the self-confidence terms; (ii) avoid the blowup by divinding the equation by the norm of matrix. We will use analytical and numerical method to investigate the modified equations. We may also look at other similar differential models in the studies of network structure and pattern formation. 

Suggested prerequisites: Math 302, CS 141

Contact: Junping Shi