Graph Isomorphism: Foundations and Algorithms

Determining whether two network structures are identical in form lies at the heart of discrete mathematics, computer vision, and computational biology. This course provides a clear, conceptual path into graph isomorphism for simple graphs, breaking down complex mathematical principles into intuitive, structured written lessons. You will gain a solid grasp of how graph isomorphism works, moving from foundational graph theory definitions to search algorithms and modern color-refinement methods. What you'll learn: - Understand foundational graph concepts, adjacency matrices, and the formal definition of isomorphism - Analyze graph invariants such as degree sequences, spectral properties, and subgraphs to differentiate structures - Implement systematic backtracking and permutation tests for exact isomorphism verification - Apply the Weisfeiler-Lehman color-refinement algorithm to test graph equivalence - Explore the computational complexity landscape of the graph isomorphism problem and its position between P and NP - Practice graph comparison workflows with modern Python implementations The course starts with essential terminology and mathematical representations before advancing through combinatorial search strategies, heuristic pruning, and algorithmic implementations through detailed written explanations and code examples. This course is built for aspiring developers, data enthusiasts, and computer science students. Basic familiarity with general programming is helpful, but no advanced graph theory background is required. Start reading today to master the theory and algorithms behind graph isomorphism.