An adjacency matrix is a square grid used to represent a graph, where each row and column corresponds to a vertex. The entries in the matrix indicate whether pairs of vertices are adjacent or not. If there is an edge connecting two vertices, the corresponding entry is marked with a 1 (or the weight of the edge), while a 0 indicates no connection. This matrix is particularly useful in computer science and mathematics for analyzing graphs, such as in algorithms for finding paths or determining connectivity. It provides a clear and compact way to visualize relationships between vertices in a graph, making it easier to perform calculations and analyses.