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The set of strongly connected components of a directed graph

is the same as the set of strongly connected components of the graph obtained by reversing all the edges of

$.$

Let

be any connected undirected graph. Let and be distinct vertices in $.$ Then, in BFS$(),$ if ends up in layer and in $,$ then the distance between and is at least

$.$

Let

be any connected undirected graph. Let and be distinct vertices in $.$ Then, in BFS$(),$ if ends up in layer and in $,$ then the distance between and is at most

$.$

Let

be any connected undirected graph. Let and be distinct vertices and let be an edge in $.$ Then, in BFS$(),$ if ends up in layer for some must be in or $.$