An incidence matrix is a mathematical representation used in graph theory to describe the relationship between vertices and edges in a graph. In this matrix, rows typically represent the vertices, while columns represent the edges. A cell in the matrix is marked to indicate whether a specific vertex is connected to a specific edge, often using binary values (1 for connection, 0 for no connection). These matrices are useful for analyzing the structure of graphs, including directed graphs and undirected graphs. They help in various applications, such as network analysis, computer science, and operations research, by providing a clear and organized way to visualize connections within a graph.