Connected Digraph

There are two distinct notions of connectivity in a directed graph. A directed graph is weakly connected if there is an undirected path between any pair of vertices, and strongly connected if there is a directed path between every pair of vertices (Skiena 1990, p. 173). The following tables summarized the number of weakly and strongly connected digraphs on , 2, ... nodes. The 8 weakly but not strongly connected digraphs on three nodes are illustrated above.

REFERENCES

Skiena, S. "Strong and Weak Connectivity." §5.1.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 172-174, 1990.

Sloane, N. J. A. Sequences A003085/M2067, A035512, and A056988 in "The On-Line Encyclopedia of Integer Sequences."