In this paper are presented methods for testing the connectedness of a finite graph and for the determination of all the trees of the same. While the tests for the connectedness furnished in this paper are stated in terms of the concopt of edge matrix, a concept introduced in the paper, the process of finding all the trees of a finite N-graph G, makes use of the cover table, which expresses the cover conditions of all the vertices of the graph G by its edges. From the cover table of G, the φGset of somo suitable partial graphs with (n — 1) edges of G is determined. Then, from the members of φGare chosen either those which are connected or those which contain no cycle and in either case the set TrGof all the trees of G is obtained. The method of finding the members of the set φGis however iterative and in this process no duplication of results occurs.