Graph Theory

This chapter covers fundamental models of random and structured graphs, with rigorous mathematical definitions and Python implementations.

Topics:

• Barabási-Albert Model — scale-free networks via preferential attachment

• Erdős-Rényi G(n,p) — classical random graphs and phase transitions

• Cayley Trees and k-Regular Trees — labeled trees, Cayley’s formula, and Bethe lattices

• Centrality and PageRank — Katz centrality, Perron-Frobenius theorem, and Google’s PageRank

• Barabási-Albert Model
• Erdős-Rényi \(G(n,p)\) Model
• Cayley Trees and \(k\)-Regular Trees
• Katz Centrality, Perron-Frobenius, and PageRank