Algebraic Graph Theory is a branch of mathematics that studies graphs using algebraic methods. It connects graph theory, which focuses on the properties and structures of graphs, with linear algebra and group theory. This field helps in understanding the relationships between graph properties and algebraic structures, such as matrices associated with graphs. Key concepts in Algebraic Graph Theory include the use of adjacency matrices, Laplacian matrices, and eigenvalues to analyze graphs. Researchers explore how these algebraic tools can reveal information about graph connectivity, coloring, and other characteristics, making it a valuable area of study in both theoretical and applied mathematics.