In this respect depth-first search (DFS) is the exact reverse process: whenever it sends a new node, it immediately continues to extend from it. It sends back to previously explored nodes only if it lay out of options. Although DFS goes to unbalanced and strange-looking exploration trees related to the orderly layers created by BFS, the combination of eager exploration with the perfect memory of a computer creates DFS very useful. It sends an algorithm template for DFS. We send special algorithms from it by specifying the subroutines traverseTreeEdge, root, init, backtrack, and traverseNonTreeEdge.

DFS creates a node when it First discovers it; started all nodes are unmarked. The main loop of DFS seems for unmarked nodes s and calls DFS(s; s) to lead a tree rooted at s. The genuine call DFS(u; v) extends all edges (v;w) out of v. The argument (u; v) display that v was reached via the edge (u; v) into v. For root nodes s, we need the .dummy. argument (s; s). We display DFS(¤; v) if the special nature of the incoming node is irrelevant for the discussion at hand. Assume now that we explore edge (v;w) within the fact DFS(¤; v). If w has been seen after, w is a node of the DFS-tree. So (v;w) is not a tree node and hence we create traverseNonTreeEdge(v;w) and prepare no recursive call of DFS. If w has not been given before, (v;w) converts a tree edge. We therefore call traverseTreeEdge(v;w), mark w and create the recursive call DFS(v;w). When we return from this call we include the next edge out of v. Once all edges out of v are included, we call backtrack on the incoming edge (u; v) to operate any summarizing or clean-up operations return and required.