A collection of trees is called a **forest**, unsurprisingly.  Your graphs are considered trees only if the edges are undirected, i.e. the relationships described are "two-way", e.g. X is related to Y can be restated validly as Y is related to X.  This is known as a symmetric binary relationship.  If your edges are directed, then the graphs are not correctly called trees.  The relationships described above are asymmetric, creating links which are also not symmetric.