HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

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) Source # Instance detailsDefined in Math.Combinatorics.Hypergraph Methods(==) :: Hypergraph a -> Hypergraph a -> Bool #(/=) :: Hypergraph a -> Hypergraph a -> Bool # Ord a => Ord (Hypergraph a) Source # Instance detailsDefined in Math.Combinatorics.Hypergraph Methodscompare :: Hypergraph a -> Hypergraph a -> Ordering #(<) :: Hypergraph a -> Hypergraph a -> Bool #(<=) :: Hypergraph a -> Hypergraph a -> Bool #(>) :: Hypergraph a -> Hypergraph a -> Bool #(>=) :: Hypergraph a -> Hypergraph a -> Bool #max :: Hypergraph a -> Hypergraph a -> Hypergraph a #min :: Hypergraph a -> Hypergraph a -> Hypergraph a # Show a => Show (Hypergraph a) Source # Instance detailsDefined in Math.Combinatorics.Hypergraph MethodsshowsPrec :: Int -> Hypergraph a -> ShowS #show :: Hypergraph a -> String #showList :: [Hypergraph a] -> ShowS #

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 :: (Eq a1, Num a2) => Hypergraph a1 -> [[a2]] Source #

fromIncidenceMatrix :: (Num a1, Enum a1, Ord a1, Num a2, Eq a2) => [[a2]] -> Hypergraph a1 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

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.

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

grid :: (Ord a, Ord b, Num a, Num b, Enum a, Enum b) => a -> b -> Hypergraph (a, b) Source #

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

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

Is this hypergraph a (projective) configuration.

The Heawood graph is the incidence graph of the Fano plane

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