how to input the adjacency matrix of a digraph to judge whether it is a simple digraph.

To input the adjacency matrix of a digraph and judge whether it is a simple digraph, follow these steps:

1. Write down the adjacency matrix of the digraph. The adjacency matrix is a square matrix where the entry in row i and column j represents the presence (or absence) of a directed edge from vertex i to vertex j. If there is an edge from i to j, the entry is 1, otherwise it is 0.

2. Check if there are any loops in the digraph. A loop is an edge that starts and ends at the same vertex. If there are any entries on the diagonal of the adjacency matrix that are non-zero, then there are loops present in the digraph.

3. Check if there are any multiple edges between two vertices. If there are any entries in the adjacency matrix that are greater than 1, then there are multiple edges between the corresponding vertices.

4. If there are no loops or multiple edges in the digraph, then it is a simple digraph. Otherwise, it is not a simple digraph.

Example: Consider the following adjacency matrix for a digraph:

0 1 0
1 0 1
0 1 0

This matrix represents a digraph with three vertices and three directed edges. There are no loops or multiple edges in this digraph, so it is a simple digraph.