The AdjacencyMatrix command returns the adjacency matrix of a graph G whose rows and columns are indexed by the vertices. The entry  of this matrix is 1 if there is an edge from vertex i to vertex j and 0 otherwise.

The default output is an n by n Matrix with the following properties:

If G is directed or undirected: datatype=anything and order=C_order

If G is undirected: shape=symmetric, storage=triangular[upper],

If G is directed: storage=rectangular, shape=[]

If G is sparse, i.e., |E| << |V|^2 then storage=sparse will be used.