Why DFS and not BFS for finding cycle in graphs

Question

Predominantly DFS is used to find a cycle in graphs and not BFS. Any reasons? Both can find if a node has already been visited while traversing the tree/graph.

Answer 1

To prove that a graph is cyclic you just need to prove it has one cycle(edge pointing towards itself either directly or indirectly).

In DFS we take one vertex at a time and check if it has cycle. As soon as a cycle is found we can omit checking other vertices.

In BFS we need to keep track of many vertex edges simultaneously and more often than not at the end you find out if it has cycle. As the size of the graph grows BFS requires more space, computation and time compared to DFS.