A weakly connected digraph is a directed graph in which it is possible to reach any node starting from any other node by traversing edges in some direction (i.e., not necessarily in the direction they point). The nodes in a weakly connected digraph therefore must all have either outdegree or indegree of at least 1. The numbers of nonisomorphic simple weakly connected digraphs on , 2, ... nodes are 1, 2, 13, 199, 9364, ... (OEIS A003085).
Weakly Connected Digraph
See alsoConnected Digraph, Strongly Connected Digraph, Weakly Connected Component
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ReferencesHarary, F. and Palmer, E. M. Graphical Enumeration. New York: Academic Press, p. 218, 1973.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. Sequence A003085/M2067 in "The On-Line Encyclopedia of Integer Sequences."
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Weisstein, Eric W. "Weakly Connected Digraph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WeaklyConnectedDigraph.html