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

TL;DR

This paper introduces a simple weighted network model to simulate how student relationships evolve in a class, highlighting the impact of initial impressions and phase transitions in hostility levels.

Contribution

It presents a novel weighted network model that captures the influence of initial conditions and phase transitions in the evolution of student relationships.

Findings

Initial impressions significantly influence final relationship distributions.

The model exhibits a phase transition based on initial amity levels.

Different initial configurations lead to varied weight distributions.

Abstract

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.