Weisfeiler-Lehman Algorithm and Graph Isomorphism Basics

Determining whether two complex network structures are fundamentally identical is a foundational challenge in computer science and data analysis. This text-based course guides you through graph isomorphism and the classical Weisfeiler-Lehman algorithm step by step. You will begin with foundational terminology in graph theory, exploring adjacency matrices, vertex labeling, and graph equivalence before examining the mechanics of iterative color refinement. By reading through structured explanations and code walk-throughs, you will understand how the Weisfeiler-Lehman test distinguishes non-isomorphic graphs and discover why it forms the theoretical backbone for modern message-passing graph neural networks (GNNs). What you will learn: Understand core graph theory concepts, vertex neighborhoods, and the graph isomorphism problem; Implement the 1-dimensional Weisfeiler-Lehman color refinement algorithm using clean Python logic; Analyze edge cases and structural limitations where standard color refinement fails; Explore higher-order k-WL algorithm extensions and their computational trade-offs; Connect algorithmic graph hashing to Weisfeiler-Lehman graph kernels for machine learning applications; Compare theoretical WL expressive power against modern message-passing neural network architectures. The course begins with foundational graph terminology and visual reasoning represented through clear text and structured data, moving sequentially toward algorithmic implementation and modern machine learning connections. This course is designed for curious beginners, programmers, and students interested in graph algorithms or machine learning theory without advanced mathematical prerequisites. Start reading today to deepen your understanding of structural graph algorithms and their modern applications.