Finite Connected Graph is Tree iff Size is One Less than Order

Theorem
Let $T$ be a connected finite simple graph of order $n$.

Then $T$ is a (finite) tree the size of $T$ is $n-1$.

Proof
By definition:
 * the order of a (finite) tree is how many nodes it has

and:
 * the size of a (finite) tree is how many edges it has.