A weighted network model for interpersonal relationship evolution

A simple model is proposed to mimic and study the evolution of interpersonal relationships in a student class. The small social group is simply assumed as an undirected and weighted graph, in which students are represented by vertices, and the depth of favor or disfavor between them are denoted by the corresponding edge weight. In our model, we find that the first impression between people has a crucial influence on the final status of student relations (i.e., the final distribution of edge weights). The system displays a phase transition in the final hostility proportion depending on the initial amity possibility. We can further define the strength of vertices to describe the individual popularity, which exhibits nonlinear evolution. Meanwhile, various nonrandom perturbations to the initial system have been investigated, and simulation results are in accord with common real-life observations.