Determine whether the networks below are isomorphic

Determine whether the networks below are isomorphic

They meet the requirements of both having the same number of vertices.

They have the same number of edges

They both have 8 vertices of degree 3.

Knowing that my knowledge tells me they are isomorphic.

But what's the best way to find out?

EDIT;

matrix for both graphs:

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

0 1 5 3 6 2 7 4
0:   1       1   1
1: 1     1     1
5:         1 1   1
3:   1     1 1
6:     1 1     1
2: 1   1 1
7:   1     1     1
4: 1   1       1


Correct?

* let $a$ correspond to $0$.
* the neighbours of $a$ are $b,f,h$. They would correspond to $1,2,4$ in some order. Again, by the symmetry of the left-hand network, it doesn't matter which order. Let $b=1$,$f=2$,$h=4$.
* $d$ is adjacent to $b$ and $f$, so $d=3$
A square $a,f,d,b$ is in the graph with another square $h,c,e,g$ where the corresponding vertices of these squares are joined in the graph. This accounts for all the edges, making the graph that of a cube.