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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.