“Depth-first search yields valuable information about the structure of a graph. Perhaps the most basic property of depth-first search is that the predecessor subgraph Gπ does indeed form a forest of trees, since the structure of the depth-first trees exactly mirrors the structure of recursive calls of DFS-VISIT. That is, u = v.π if and only if DFS-VISIT(G, v) was called during a search of u’s adjacency list. Additionally, vertex v is a descendant of vertex u in the depth-first forest if and only