hypergraph (823B)
1 # Hypergraph 2 3 generalizes [graph] 4 5 ## Basic definitions 6 7 - [vertex] 8 - [hyperedge] 9 - [primal_graph] aka "Gaifman graph" 10 - [subhypergraph] 11 12 ## Classes 13 14 - [hypergraph_uniform] 15 - [hypergraph_reduced] "reduced": no incomparable edges 16 - [hypergraph_laminar]: cf [delpia2018multilinear] 17 - [fagin1983degrees]: degrees of acyclicity 18 - also [degree_of_acyclicity]: [alpha_acyclic], etc. 19 - cyclic hypergraph contains one of: 20 - (k,k-1)-hyperclique: k vertices, each k-1 contains an edge 21 - cf [hypergraph_conformal] 22 - induced k-cycle 23 - [hypergraph_balanced] 24 - [koenig_property] 25 26 ## Problems 27 28 - [hyperclique_detection] / [hyperclique_hypothesis] 29 30 See also: [generalized_hypertree_width], [conjunctive_query], [relational_instance], [simplicial_complex] 31 32 Up: [data_structure], [computer_science] 33 34 Aliases: hypergraphs