I was reading CLRS about BFS and DFS, and the algorithms presented therein, which I take to be somewhat standard, constructs a forest in DFS that includes all the nodes, whereas BFS only constructs a tree from a chosen node $s$, and leaves out all the other nodes that are not reachable from $s$.

It seems the BFS can be adapted to construct other trees to include non-reachable nodes from $s$ and form a "BFS forest", analogous to operation of the DFS. What is the reason for constructing a forest in DFS, but only a tree (that excludes unreachable nodes) in BFS?

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• There is probably no reason; it's arbitrary. – Raphael Dec 4 '16 at 2:15
• – Raphael Dec 4 '16 at 2:16