Connectivity
If x e V and y e V, x = y, then x and y are connected if there exists a path p = v1…vn such that x = v1 and y = vn.
For G undirected, a subset S of V is a connected component if for any two distinct vertices, x e S, y e S, x is connected to y.
For G directed, a subset S of V is strongly connected if for each pair of distinct vertices (vi,vj) e S, vi is connected to vj and vj is connected to vi. S is weakly connected if either vi is connected to vj or vj is connected to vi.