A Model of Weighted Network: the Student Relationships in a Class

A simple model is proposed to simulate the evolution of interpersonal relationships in a class. The small social network is simply assumed as an undirected and weighted graph, in which students are represented by vertices, and the extent of favor or disfavor between two of them are denoted by the weight of corresponding edge. Various weight distributions have been found by choosing different initial configurations. Analysis and experimental results reveal that the effect of first impressions has a crucial influence on the final weight distribution. The system also exhibits a phase transition in the final hostility (negative weights) proportion depending on the initial amity (positive weights) proportion.