If two graphs are isomorphic, then if we represent one of them as an matrix, we can find an adjacency matrix for the other which is identical, except for the names of the nodes and edges.

An adjacency matrix for the left graph is:

```
A B C D E F G
A: 1 1 1
B: 1 1 1
C: 1 1
D: 1 1 1
E: 1 1 1
F: 1 1
G: 1 1 1
```

If we identify the vertices as (A B C D E F G) = (7 4 3 6 5 2 1), and write down the adjacency matrix for the second graph in that order, we get the same matrix:

```
7 4 3 6 5 2 1
7: 1 1 1
4: 1 1 1
3: 1 1
6: 1 1 1
5: 1 1 1
2: 1 1
1: 1 1 1
```

Of course, the objects are not isomorphic if the names of the vertices are considered significant in the representation. Or if there are constraints, such as that A must be identified with node 1 (because, say, the graph are part of some larger object, and how they connect to it is not negotiable).

Two entities that are considered isomorphic are never identical unless they are the same entity.

An isomorphism is always based on caring about some possible differences, while declaring that others do not matter.