No vertices:

No edges:
        0        0        0
        0        0        0
        0        0        0

Disconnected graph with loops and multiple edges:
        0        1        1        0        0        0
        0        1        0        1        0        0
        1        0        0        1        0        0
        0        0        0        0        2        0
        0        0        0        0        0        0
        0        0        0        0        0        0

Same graph, undirected, symmetric matrix:
        0        1        2        0        0        0
        1        1        0        1        0        0
        2        0        0        1        0        0
        0        1        1        0        2        0
        0        0        0        2        0        0
        0        0        0        0        0        0

Same graph, undirected, upper triangular matrix:
        0        1        2        0        0        0
        0        1        0        1        0        0
        0        0        0        1        0        0
        0        0        0        0        2        0
        0        0        0        0        0        0
        0        0        0        0        0        0

Same graph, undirected, lower triangular matrix:
        0        0        0        0        0        0
        1        1        0        0        0        0
        2        0        0        0        0        0
        0        1        1        0        0        0
        0        0        0        2        0        0
        0        0        0        0        0        0