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.

- combinationsOf :: Integral t => t -> [a] -> [[a]]
- data Graph a = G [a] [[a]]
- graph :: Ord t => ([t], [[t]]) -> Graph t
- nullGraph :: Graph Int
- c :: Integral t => t -> Graph t
- k :: Integral t => t -> Graph t
- fromDigits :: Integral a => Graph [a] -> Graph a
- fromBinary :: Integral a => Graph [a] -> Graph a
- diameter :: Ord t => Graph t -> Int
- girth :: Eq t => Graph t -> Int
- kneser :: Integral t => t -> t -> Graph [t]

# Documentation

combinationsOf :: Integral t => t -> [a] -> [[a]]Source

combinationsOf k xs returns the subsets of xs of size k. If xs is in ascending order, then the returned list is in ascending order

Datatype for graphs, represented as a list of vertices and a list of edges. Both the list of vertices and the list of edges, and also the 2-element lists representing the edges, are required to be in ascending order, without duplicates.

G [a] [[a]] |

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

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

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

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 aSource

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.

diameter :: Ord t => Graph t -> IntSource

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