====== Chapter 3.5: Connectivity in Directed Graphs ======
In order to represent a directed graph, it is best to use an adjacency lists. Each node can have 2 lists associated with it: a list of nodes it points to and a list of nodes that point to it. Graph search algorithms (BFS & DFS) are basically the same for a directed graph as they are for an undirected graph. BFS starts at a node //s// and works outwardly, in the same way it would for an undirected graph. The algorithm still runs in O(n+m) time. However, BFS computes the set of all nodes for which there is a path from //s// to a node //t//, and this doesn't run both ways. There may or may not be a path from a node //t// back to //s//. DFS runs similarly.

A directed graph is **strongly connected** if for every two nodes //u// and //v//, there is a path from //u// to //v// and a path from //v// to //u//. When there is a path from //u// to //v// and a path from //v// to //u//, we can call nodes //u// and //v// **mutually reachable**. So a graph is strongly connected if every pair of nodes is mutually reachable.

If //u// and //v// are mutually reachable and //v// and //w// are mutually reachable, then //v// and //w// are mutually reachable.

In a directed graph, the **strong component** is the set of all //v// such that //s// and //v// are mutually reachable. For any two nodes //s// and //t// in a directed graph, their strong components are either identical or disjoint.

I'd rate this section a 10! It was very easy to read and understand.