Strongly Connected Components

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 $\in$ V, there is a path ($\leadsto$) from u to v (u $\leadsto$ v) and from v to u (v $\leadsto$ u).

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

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

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