Mathematical Modeling of Social Networks: A Graph Theoretical Approach

Abstract

Social networks play a vital role in shaping information dissemination and interaction dynamics in modern societies. Understanding the structural properties of such networks is essential for identifying influential individuals and optimizing communication strategies. This study presents a graph-theoretical framework for modeling and analyzing social networks using a real-life–inspired university social system. The network is represented as an undirected graph, where nodes correspond to individuals and edges represent academic interactions. To address privacy and ethical concerns, synthetic data is employed to simulate realistic interaction patterns. Classical graph-theoretical measures, including degree, betweenness, and closeness centrality, are utilized to evaluate node importance and influence. The analysis reveals that nodes with high centrality values significantly enhance information dissemination efficiency within the network. The proposed approach demonstrates the effectiveness of graph theory as a mathematical tool for analyzing social structures and provides a transparent, application-oriented methodology suitable for both research and educational purposes. The study further highlights the potential for extending the framework to dynamic, weighted, and uncertainty-based graph models.