algebraic graph theory

Algebraic graph theory is a branch of mathematics that studies graphs—structures made of points (vertices) connected by lines (edges)—using tools from algebra. It examines patterns and properties of graphs through matrices and algebraic operations, helping to analyze complex networks like social connections, communication systems, or molecular structures. By translating graphs into algebraic forms, researchers can uncover insights about their symmetry, connectivity, and behavior, enabling a deeper understanding of both theoretical and real-world network systems.