HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellNone
LanguageHaskell98

Math.Combinatorics.Hypergraph

Description

A module defining a type for hypergraphs.

Synopsis

Documentation

data Hypergraph a Source

Constructors

H [a] [[a]] 

Instances

Eq a => Eq (Hypergraph a) 
Ord a => Ord (Hypergraph a) 
Show a => Show (Hypergraph a) 

hypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a Source

toHypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a Source

isUniform :: Ord a => Hypergraph a -> Bool Source

Is this hypergraph uniform - meaning that all blocks are of the same size

same :: Eq a => [a] -> Bool Source

incidenceMatrix :: (Num t, Eq a) => Hypergraph a -> [[t]] Source

fromIncidenceMatrix :: (Ord a1, Num a1, Num a, Eq a, Enum a1) => [[a]] -> Hypergraph a1 Source

isProjectivePlane :: Ord a => Hypergraph a -> Bool Source

Is this hypergraph a projective plane - meaning that any two lines meet in a unique point, and any two points lie on a unique line

isProjectivePlaneTri :: Ord a => Hypergraph a -> Bool Source

Is this hypergraph a projective plane with a triangle. This is a weak non-degeneracy condition, which eliminates all points on the same line, or all lines through the same point.

isProjectivePlaneQuad :: Ord a => Hypergraph a -> Bool Source

Is this hypergraph a projective plane with a quadrangle. This is a stronger non-degeneracy condition.

grid :: (Ord t1, Ord t, Num t1, Num t, Enum t1, Enum t) => t -> t1 -> Hypergraph (t, t1) Source

dualGrid :: Integral a => a -> a -> Hypergraph a Source

isConfiguration :: Ord a => Hypergraph a -> Bool Source

Is this hypergraph a (projective) configuration.

heawoodGraph :: Graph (Either Integer [Integer]) Source

The Heawood graph is the incidence graph of the Fano plane

tutteCoxeterGraph :: Graph (Either [Integer] [[Integer]]) Source

The Tutte-Coxeter graph, also called the Tutte 8-cage