Safe Haskell	None
Language	Haskell98

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

fromGraph :: Graph a -> Hypergraph a Source

fromDesign :: Ord a => Design a -> Hypergraph a Source

incidenceGraph :: Ord a => Hypergraph a -> Graph (Either a [a]) 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

isPartialLinearSpace :: Ord a => Hypergraph a -> Bool 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.

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

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

isGenQuadrangle' :: Ord a => Hypergraph a -> Bool Source

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

Is this hypergraph a (projective) configuration.

fanoPlane :: Hypergraph Integer Source

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

The Heawood graph is the incidence graph of the Fano plane

desarguesConfiguration :: Hypergraph [Integer] Source

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

pappusConfiguration :: Hypergraph Integer Source

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

coxeterGraph :: Graph [Integer] Source

duads :: [[Integer]] Source

synthemes :: [[[Integer]]] Source

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

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

intersectionGraph :: Ord a => Hypergraph a -> Graph [a] Source