I've decided to refresh my graph theory using CLRS 4th edition. They define a free tree as a connected, acyclic, undirected graph. None of these conditions prevent us from having null graph with zero vertices and zero edges.
On page 1170, it is proven that for a free tree, |E| = |V| - 1. We can derive contradiction from it: |0| = |0| - 1 -> 0 = -1