An adjacency matrix is a mathematical representation used to describe the connections between nodes in a graph. In this matrix, rows and columns represent the nodes, and the entries indicate whether pairs of nodes are connected. A value of 1 typically signifies a direct connection, while a value of 0 indicates no connection. This format is particularly useful for analyzing relationships in networks, such as social networks or transportation systems. Adjacency matrices can be used for both directed and undirected graphs. In a directed graph, the matrix shows the direction of connections, while in an undirected graph, the connections are bidirectional. This tool is essential in fields like computer science, graph theory, and network analysis for efficiently processing and visualizing relationships.