The Evolution of Interpersonal Relationships in a Social Group
  A model has been proposed to simulate the evolution of interpersonal relationships in a social group. The small social community is simply assumed as an undirected and weighted graph, where individuals are denoted by vertices, and the extent of favor or disfavor between them are represented by the corresponding edge weight. One could further define the strength of vertices to describe the individual popularity. The strength evolution exhibits a nonlinear behavior. Meanwhile, various acute perturbations to the system have been investigated. In the framework of our model, it is also interesting to study the adaptive process of a new student joining a class midway. 
Bo Hu, Xin-Yu Jiang, Bing-Hong Wang, Jun-Feng Ding, Tao-Zhou, Yan-Bo   Xie