A symmetric adjacency matrix like this can be used to create an undirected graph:
graph = [0 1 1 0 0;
1 0 0 1 0;
1 0 0 1 1;
0 1 1 0 1;
0 0 1 1 0]
To draw your (asymmetric) matrix, use a directed graph:
graph = [
0 2 4 0 0 0 ;
0 0 1 7 0 0 ;
0 0 0 0 3 0 ;
0 0 0 0 0 1 ;
0 0 0 2 0 5 ;
0 0 0 0 0 0 ]
g = SimpleDiGraph(graph)