data-structures Graph traversals Depth First Search


Example

Depth First Traversal (or Search) for a graph is similar to Depth First Traversal of a tree. The only catch here is, unlike trees, graphs may contain cycles, so we may come to the same node again. To avoid processing a node more than once, we use a boolean visited array.

Below algorithm presents the steps for graph traversal using DFS:

Algorithm DFS(v);

Input: A vertex v in a graph

Output: A labeling of the edges as “discovery” edges and “backedges”

for each edge e incident on v do

    if edge e is unexplored then

    let w be the other endpoint of e
    if vertex w is unexplored then
        label e as a discovery edge
        recursively call DFS(w)
    else
    label e as a backedge

DFS Illustration

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