A007984 Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).

1, 2, 11, 185, 8782, 1067825, 312510571, 212133402500, 326266056291213, 1118902054495975181, 8455790399687227104576, 139537050182278289405732939, 4991058955493997577840793161279

Offset: 1

Author

David Madigan (madigan(AT)stat.washington.edu)

Keywords

• nonn

References

• S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Proc. of Conf. on Uncertainty in Artificial Intelligence (2001), 171-177.
• S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Artificial Intelligence, 141 (2002), 137-155.
• Bertran Steinsky, Enumeration of Labelled Essential Graphs, Ars Comb., 111, (2013), 485-494

Links

• S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Univ. of Washington, Dept. of Statistics, Technical Reports.
• S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Univ. of Washington, Dept. of Statistics, Technical Reports.
• Zehao Jin, Mario Pasquato, Benjamin L. Davis, Tristan Deleu, Yu Luo, Changhyun Cho, Pablo Lemos, Laurence Perreault-Levasseur, Yoshua Bengio, Xi Kang, Andrea Valerio Maccio, and Yashar Hezaveh, A Data-driven Discovery of the Causal Connection between Galaxy and Black Hole Evolution, arXiv:2410.00965 [astro-ph.GA], 2024. See p. 33.
• Zehao Jin, Mario Pasquato, Benjamin L. Davis, Tristan Deleu, Yu Luo, Changhyun Cho, Pablo Lemos, Laurence Perreault-Levasseur, Yoshua Bengio, and Xi Kang, Causal Discovery in Astrophysics: Unraveling Supermassive Black Hole and Galaxy Coevolution, Astrophys. J. (2025) Vol. 979, 212. See Fig. 7.

Crossrefs

Cf. A368569 (refined by # arcs).

Extensions

More terms from Steven B. Gillispie (gillisp(AT)u.washington.edu), Oct 21 2003

a(10) corrected by Steven B. Gillispie (gillisp(AT)u.washington.edu), Aug 14 2007, who says: I have learned from Bertran Steinsky (who determined the correct number) that there was an error in my computer software that computed a(10). The correct value is 1118902054495975181.

a(11)-a(13) from Bertran Steinsky, Jun 24 2013