Graph representation is a way to visually or mathematically depict relationships between objects, known as vertices or nodes, connected by edges. This structure is commonly used in computer science, mathematics, and various fields to model networks, such as social connections, transportation systems, and communication pathways. There are several methods for representing graphs, including adjacency lists and adjacency matrices. An adjacency list uses a list to show which vertices are connected, while an adjacency matrix uses a grid to indicate connections between all pairs of vertices. These representations help in analyzing and solving problems related to graphs efficiently.