Comparative Analysis of Random Graph Models for Power-Law Networks

This thesis presents a comparative study of three classical random graph models, Erdős-Rényi (ER), Barabási-Albert (BA), and the copying model, to evaluate their capacity to generate power-law degree distributions commonly observed in real-world networks. We begin with an overview of the power law and scale-free networks, followed by analytical derivations that examine the generative mechanisms, structural properties, and theoretical degree distributions of each model. We then simulate these models and analyze their respective strengths and limitations in capturing the power-law characteristics of complex networks.