Relation of Adjacency matrices of 2 graphs

Question

Let G be the subgraph of G¯(prime) such that there is an edge between v_i ∈ V and v_j ∈ V in G if and only if there is at least one edge between v_i and v_j in G¯(prime).

Any tips or hint to solve about finding A from A¯(prime) ?

Answer 1

$A_{ij}$ is equal to 1 if $\bar A_{ij}$ is not equal to zero. This means that there is an edge between $v_i$ and $v_j$ on $G$ if there is at least one edge between them on $\bar G$, as stated in the problem. $A_{ij}$ is zero if $i=j$ or $\bar A_{ij}=0$.

$$A_{ij}=\begin{cases}0 & i=j\textrm{ or }\bar A_{ij}=0\\1 & \bar A_{ij}>0\end{cases}$$