The breadth-first traversal enqueues each node in the graph at most once. When a node is dequeued, all the edges emanating from that node are considered. Therefore, a complete traversal enumerates every edge in the graph.

The actual running time of the breadth-first traversal routine depends on the graph representation scheme used. The worst-case running time for the traversal of a graph represented using an adjacency matrix is

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

If the graph is sparse, then . Therefore, if a sparse graph is represented using adjacency lists and if , the worst-case running time of the breadth-first traversal is just .

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