Williamson's Theorem is a result in the field of mathematics, specifically in the area of graph theory. It provides a criterion for determining when a certain type of graph can be represented as a distance-regular graph. This theorem is significant because it helps mathematicians understand the structure and properties of graphs that exhibit regularity in their distances between vertices. The theorem states that if a graph satisfies specific conditions related to its diameter and the number of vertices, it can be classified as a distance-regular graph. This classification aids in the study of combinatorial designs and has applications in various fields, including network theory and coding theory.