Safe Haskell | None |
---|---|

Language | Haskell98 |

A module defining a polymorphic data type for (simple, undirected) graphs, together with constructions of some common families of graphs, new from old constructions, and calculation of simple properties of graphs.

- set :: Ord b => [b] -> [b]
- powerset :: [t] -> [[t]]
- data Graph a = G [a] [[a]]
- nf :: Ord a => Graph a -> Graph a
- isSetSystem :: Ord a => [a] -> [[a]] -> Bool
- isGraph :: Ord a => [a] -> [[a]] -> Bool
- graph :: Ord t => ([t], [[t]]) -> Graph t
- toGraph :: Ord a => ([a], [[a]]) -> Graph a
- vertices :: Graph t -> [t]
- edges :: Graph t -> [[t]]
- incidenceMatrix :: (Num t, Eq a) => Graph a -> [[t]]
- fromIncidenceMatrix :: (Ord t, Num t, Num a, Eq a, Enum t) => [[a]] -> Graph t
- adjacencyMatrix :: (Ord a, Num t) => Graph a -> [[t]]
- fromAdjacencyMatrix :: (Num b, Eq b) => [[b]] -> Graph Int
- nullGraph :: Integral t => t -> Graph t
- nullGraph' :: Graph Int
- c :: Integral t => t -> Graph t
- k :: Integral t => t -> Graph t
- kb :: Integral t => t -> t -> Graph t
- kb' :: Integral t => t -> t -> Graph (Either t t)
- q :: Integral t => Int -> Graph t
- q' :: Integral t => Int -> Graph [t]
- tetrahedron :: Graph Integer
- cube :: Graph Integer
- octahedron :: Graph Integer
- dodecahedron :: Graph Integer
- icosahedron :: Graph Integer
- prism :: Int -> Graph (Int, Int)
- to1n :: (Ord t, Ord a, Num t, Enum t) => Graph a -> Graph t
- fromDigits :: Integral a => Graph [a] -> Graph a
- fromBinary :: Integral a => Graph [a] -> Graph a
- petersen :: Graph [Integer]
- complement :: Ord t => Graph t -> Graph t
- restriction :: Eq a => Graph a -> [a] -> Graph a
- inducedSubgraph :: Eq a => Graph a -> [a] -> Graph a
- lineGraph :: (Ord a, Ord t, Num t, Enum t) => Graph a -> Graph t
- lineGraph' :: Ord a => Graph a -> Graph [a]
- cartProd :: (Ord t1, Ord t) => Graph t -> Graph t1 -> Graph (t, t1)
- order :: Graph a -> Int
- size :: Graph t -> Int
- valency :: Eq a => Graph a -> a -> Int
- valencies :: Eq a => Graph a -> [(Int, Int)]
- valencyPartition :: Eq b => Graph b -> [[b]]
- regularParam :: Eq a => Graph a -> Maybe Int
- isRegular :: Eq t => Graph t -> Bool
- isCubic :: Eq t => Graph t -> Bool
- nbrs :: Eq a => Graph a -> a -> [a]
- findPaths :: Eq a => Graph a -> a -> a -> [[a]]
- distance :: Eq a => Graph a -> a -> a -> Int
- diameter :: Ord t => Graph t -> Int
- findCycles :: Eq a => Graph a -> a -> [[a]]
- girth :: Eq t => Graph t -> Int
- distancePartition :: Ord a => Graph a -> a -> [[a]]
- distancePartitionS :: Ord a => [a] -> Set [a] -> a -> [[a]]
- component :: Ord a => Graph a -> a -> [a]
- isConnected :: Ord t => Graph t -> Bool
- components :: Ord a => Graph a -> [[a]]
- j :: Int -> Int -> Int -> Graph [Int]
- kneser :: Int -> Int -> Graph [Int]
- johnson :: Int -> Int -> Graph [Int]
- bipartiteKneser :: Int -> Int -> Graph (Either [Int] [Int])
- desargues1 :: Graph (Either [Int] [Int])
- gp :: Integral a => a -> a -> Graph (Either a a)
- petersen2 :: Graph (Either Integer Integer)
- prism' :: Integral a => a -> Graph (Either a a)
- durer :: Graph (Either Integer Integer)
- mobiusKantor :: Graph (Either Integer Integer)
- dodecahedron2 :: Graph (Either Integer Integer)
- desargues2 :: Graph (Either Integer Integer)

# Documentation

Datatype for graphs, represented as a list of vertices and a list of edges. For most purposes, graphs are required to be in normal form. A graph G vs es is in normal form if (i) vs is in ascending order without duplicates, (ii) es is in ascending order without duplicates, (iii) each e in es is a 2-element list [x,y], x<y

G [a] [[a]] |

nf :: Ord a => Graph a -> Graph a Source

Convert a graph to normal form. The input is assumed to be a valid graph apart from order

isSetSystem :: Ord a => [a] -> [[a]] -> Bool Source

graph :: Ord t => ([t], [[t]]) -> Graph t Source

Safe constructor for graph from lists of vertices and edges. graph (vs,es) checks that vs and es are valid before returning the graph.

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

adjacencyMatrix :: (Ord a, Num t) => Graph a -> [[t]] Source

nullGraph :: Integral t => t -> Graph t Source

The null graph on n vertices is the graph with no edges

nullGraph' :: Graph Int Source

The null graph, with no vertices or edges

kb :: Integral t => t -> t -> Graph t Source

kb m n is the complete bipartite graph on m and n vertices

kb' :: Integral t => t -> t -> Graph (Either t t) Source

kb' m n is the complete bipartite graph on m left and n right vertices

fromDigits :: Integral a => Graph [a] -> Graph a Source

Given a graph with vertices which are lists of small integers, eg [1,2,3], return a graph with vertices which are the numbers obtained by interpreting these as digits, eg 123. The caller is responsible for ensuring that this makes sense (eg that the small integers are all < 10)

fromBinary :: Integral a => Graph [a] -> Graph a Source

Given a graph with vertices which are lists of 0s and 1s, return a graph with vertices which are the numbers obtained by interpreting these as binary digits. For example, [1,1,0] -> 6.

complement :: Ord t => Graph t -> Graph t Source

restriction :: Eq a => Graph a -> [a] -> Graph a Source

The restriction of a graph to a subset of the vertices

inducedSubgraph :: Eq a => Graph a -> [a] -> Graph a Source

lineGraph' :: Ord a => Graph a -> Graph [a] Source

valencyPartition :: Eq b => Graph b -> [[b]] Source

isRegular :: Eq t => Graph t -> Bool Source

A graph is regular if all vertices have the same valency (degree)

distance :: Eq a => Graph a -> a -> a -> Int Source

Within a graph G, the distance d(u,v) between vertices u, v is length of the shortest path from u to v

diameter :: Ord t => Graph t -> Int Source

The diameter of a graph is maximum distance between two distinct vertices

findCycles :: Eq a => Graph a -> a -> [[a]] Source

girth :: Eq t => Graph t -> Int Source

The girth of a graph is the size of the smallest cycle that it contains. Note: If the graph contains no cycles, we return -1, representing infinity.

distancePartition :: Ord a => Graph a -> a -> [[a]] Source

distancePartitionS :: Ord a => [a] -> Set [a] -> a -> [[a]] Source

isConnected :: Ord t => Graph t -> Bool Source

Is the graph connected?

components :: Ord a => Graph a -> [[a]] Source