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A001174 Number of oriented graphs (i.e., digraphs with no bidirected edges) on n unlabeled nodes. Also number of complete digraphs on n unlabeled nodes. Number of antisymmetric relations (i.e., oriented graphs with loops) on n unlabeled nodes is A083670.
(Formerly M1809 N0715)
1, 2, 7, 42, 582, 21480, 2142288, 575016219, 415939243032, 816007449011040, 4374406209970747314, 64539836938720749739356, 2637796735571225009053373136, 300365896158980530053498490893399 (list; graph; refs; listen; history; text; internal format)



F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 133, c_p.

M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, pp. 14-22.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..14.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

R. L. Davis, The number of structures of finite relations, Proc. Amer. Math. Soc. 4 (1953), 486-495.

F. Harary and E. M. Palmer, Enumeration of mixed graphs, Proc. Amer. Math. Soc., 17 (1966), 682-687.

T. R. Hoffman, J. P. Solazzo, Complex Two-Graphs via Equiangular Tight Frames, arXiv preprint arXiv:1408.0334, 2014

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

Eric Weisstein's World of Mathematics, Oriented Graph


There's an explicit formula - see for example Harary and Palmer (book), Eq. (5.4.14).


Cf. A000595, A001173.

Cf. A047656 (labeled case), A054941 (connected labeled case), A086345 (connected unlabeled case).

Sequence in context: A091669 A108042 A152559 * A067975 A065298 A091877

Adjacent sequences:  A001171 A001172 A001173 * A001175 A001176 A001177




N. J. A. Sloane


More terms from Vladeta Jovovic

Revised description from Vladeta Jovovic, Jan 20 2005



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Last modified July 31 11:39 EDT 2015. Contains 260165 sequences.