Problem $1.(14$ points$)$ Draw the directed graph represented by the adjacency matrix A below.

Then draw a BFS tree starting from the first node $($corresponding to the first row$).$ When visiting

neighbors of a certain node, you can follow nodes in any order. Is the BFS tree you returned unique

for this instance? Explain why or why not.

$A=\left[\begin{array}{ccccccc}0& 1& 0& 0& 1& 0& 0\\ 0& 0& 1& 0& 0& 1& 0\\ 1& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 1\\ 0& 1& 0& 0& 0& 0& 0\end{array}\right]$