An adjacency matrix is a square matrix that is used to represent a graph. The rows and columns of the matrix are labeled as per the graph vertices. So, if the graph vertices are 1,2,...5, then the rows and columns of the adjacency matrix will be labeled as 1,2,...5. Initially, the matrix is filled with all zeros (0). Then, the 0 at the mat[i][j] location (where i and j refer to the vertices) is replaced by 1 if there is an edge between the vertices of i and j. For example, if there is an edge from vertex 2 to vertex 3, then at the mat[2][3] index location, the value of 0 will be replaced by 1. In short, the elements of the adjacency matrix indicate whether pairs of vertices are adjacent or not in the graph.
Consider the following directed graph:
Its adjacency matrix representation is as follows...