Foundations of Graph Theory and Network Analysis

From search engines and social networks to GPS routing and molecular biology, our interconnected world relies on the mathematical principles of graph theory. Understanding how to model relationships as nodes and edges is a crucial skill for computer scientists, data analysts, and software developers. This text-based course takes you from absolute beginner to confidently analyzing complex networks. You will learn to translate real-world problems into mathematical graphs, understand the fundamental algorithms that power modern technology, and apply these concepts to solve practical routing and connectivity challenges. What you'll learn: - Understand foundational terminology, including vertices, edges, directed graphs, and weighted networks. - Analyze classical graph problems such as the Eulerian path, Hamiltonian cycles, and the Traveling Salesperson Problem. - Apply core traversal algorithms like Breadth-First Search (BFS) and Depth-First Search (DFS) to determine connectivity. - Calculate shortest routes using Dijkstra's algorithm and understand its application in modern routing systems. - Explore modern applications of graph theory in social network analysis, recommendation engines, and basic graph databases. - Practice modeling real-world scenarios, such as scheduling and infrastructure design, using formal graph representations. The course begins with core definitions and fundamental structures before progressing systematically through paths, trees, optimization algorithms, and modern network analysis. Each section features detailed written explanations, clear code snippets, and conceptual exercises to solidify your understanding. Designed for beginners in computer science, mathematics, or data analysis, this course requires no prior knowledge of advanced math or programming. Start reading today to unlock the power of network-based thinking and algorithmic problem-solving.