Given below is information about a network. Choose one of the following three options: the network is definitely a tree; the network is definitely not a tree; the network may or may not be a tree $($more information is needed$).$ Accompany your answer with a brief explanation for your choice.

The network has $9$ vertices and $8$ edges.

Choose the correct answer below.

A$.$ The network is definitely not a tree because it violates the $N-1$ edges property.

B$.$ The network is definitely a tree because it satisfies the $N+1$ edges property.

C$.$ The network is definitely a tree because it satisfies the $N-1$ edges property.

D$.$ The network may or may not be a tree because the number of circuits is unknown.

E$.$ The network is definitely a tree because it satisfies the no$-$bridges property.

F$.$ The network may or may not be a tree because the number of bridges is unknown.

G$.$ The network is definitely not a tree because it violates the single$-$path property.

H$.$ The network is definitely not a tree because it violates the $N+1$ edges property.