The running time of the depth-first traversal routine depends on the graph representation scheme used. The traversal visits each node in the graph at most once. When a node is visited, all the edges emanating from that node are considered. During a complete traversal enumerates every edge in the graph.

Therefore, the worst-case running time for the depth-first traversal of a graph is represented using an adjacency matrix is

When adjacency lists are used, the worst case running time for the depth-first traversal routine is

Recall that for a sparse graph graph . If the sparse graph is represented using adjacency lists and if and the worst-case running time of the depth-first traversal is simply .

Copyright © 1997 by Bruno R. Preiss, P.Eng. All rights reserved.