Many graph applications look for a minimal way to connect each vertex to every other vertex.

Examples: bridging gaps, identifying bottlenecks

A graph G = (V, E) is strongly connected if for every pair of vertices <u,v>, u,v V, there is a path () from u to v (u v) and from v to u (v u).

A strongly connected component (SCC) of a graph G = (V, E) is a maximal set U V such that for every pair <u,v> U, u v and v u.

**Define:** The transpose of graph G = (V, E) is the graph
, where
.

Time to create *G*^{T} = O(V+E)