First graph was given by its adjacency matrix, While the second one was given by its edges coordinates, as the theory says graphs are isomorphic by the number of their nodes (one of the signs), as can be seen both have the same number of the nodes, but my professor wants me to find 1-to-1 correspondence between these two graphs, how can it be done? 
Observation from degree-counting:
In both graphs there are 2 vertices with degree 4.
In the upper graph: vertex $0$ is adjacent to vertices $2,4,5,\mathbf{6}$ and vertex $3$ is adjacent to $1,\mathbf{2},5,6$.
In the lower graph: vertex $7$ is adjacent to $\mathbf{1},2,4,5$ and vertex $3$ is adjacent to $1,\mathbf{4},5,6$.
Here I've highlighted the difference from the lower and upper graphs. So you may be able to find an isomorphism by renaming a few vertices. Possibly $0 \to 7, 6 \to 1, 2 \to 4$. (upper $\to$ lower)
In the upper graph, $7$ is adjacent to $1,5,6$, and in the lower graph $8$ is adjacent to $1,5,6$. In the upper graph, $5$ is adjacent to $0,3,7$, and in the lower graph $5$ is adjacent to $8,3,7$, matching our hypothesis of $7 \to 8$ and $5 \to 5$. Similar reasoning supports $3 \to 3$.