vertex package:algebraic-graphs

Construct the graph comprising a single isolated vertex. An alias for the constructor Vertex.

isEmpty     (vertex x) == False
hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0
size        (vertex x) == 1

vertex :: a -> AdjacencyMap a

algebraic-graphs Algebra.Graph.Acyclic.AdjacencyMap Algebra.Graph.AdjacencyMap

Construct the graph comprising a single isolated vertex.

isEmpty     (vertex x) == False
hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0

vertex :: Int -> AdjacencyIntMap

algebraic-graphs Algebra.Graph.AdjacencyIntMap

Construct the graph comprising a single isolated vertex.

isEmpty     (vertex x) == False
hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0

vertex :: Either a b -> AdjacencyMap a b

algebraic-graphs Algebra.Graph.Bipartite.AdjacencyMap

Construct the graph comprising a single isolated vertex.

vertex . Left  == leftVertex
vertex . Right == rightVertex

vertex :: Graph g => Vertex g -> g

algebraic-graphs Algebra.Graph.Class

Construct the graph with a single vertex.

vertex :: Graph g => a -> g a

algebraic-graphs Algebra.Graph.HigherKinded.Class

Construct the graph comprising a single isolated vertex. An alias for pure.

vertex :: a -> Graph e a

algebraic-graphs Algebra.Graph.Labelled

Construct the graph comprising a single isolated vertex. An alias for the constructor Vertex.

isEmpty     (vertex x) == False
hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0

vertex :: a -> AdjacencyMap e a

algebraic-graphs Algebra.Graph.Labelled.AdjacencyMap

Construct the graph comprising a single isolated vertex.

isEmpty     (vertex x) == False
hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0

vertex :: a -> Graph a

algebraic-graphs Algebra.Graph.NonEmpty

Construct the graph comprising a single isolated vertex. An alias for the constructor Vertex.

hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0
size        (vertex x) == 1

vertex :: a -> AdjacencyMap a

algebraic-graphs Algebra.Graph.NonEmpty.AdjacencyMap

Construct the graph comprising a single isolated vertex.

hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0

vertex :: a -> Relation a

algebraic-graphs Algebra.Graph.Relation Algebra.Graph.Relation.Symmetric

Construct the graph comprising a single isolated vertex.

isEmpty     (vertex x) == False
hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0

vertex :: a -> Graph a

algebraic-graphs Algebra.Graph.Undirected

Construct the graph comprising a single isolated vertex.

isEmpty     (vertex x) == False
hasVertex x (vertex y) == (x == y)
vertexCount (vertex x) == 1
edgeCount   (vertex x) == 0
size        (vertex x) == 1

Vertex :: a -> Graph a

algebraic-graphs Algebra.Graph Algebra.Graph.NonEmpty

type family Vertex g

algebraic-graphs Algebra.Graph.Class

Vertex :: a -> Graph e a

algebraic-graphs Algebra.Graph.Labelled

vertexCount :: Ord a => Graph a -> Int

algebraic-graphs Algebra.Graph

The number of vertices in a graph. Complexity: O(s * log(n)) time. Good consumer.

vertexCount empty             ==  0
vertexCount (vertex x)        ==  1
vertexCount                   ==  length . vertexList
vertexCount x < vertexCount y ==> x < y

vertexList :: Ord a => Graph a -> [a]

algebraic-graphs Algebra.Graph

The sorted list of vertices of a given graph. Complexity: O(s * log(n)) time and O(n) memory. Good consumer of graphs and producer of lists.

vertexList empty      == []
vertexList (vertex x) == [x]
vertexList . vertices == nub . sort

vertexSet :: Ord a => Graph a -> Set a

algebraic-graphs Algebra.Graph

The set of vertices of a given graph. Complexity: O(s * log(n)) time and O(n) memory. Good consumer.

vertexSet empty      == Set.empty
vertexSet . vertex   == Set.singleton
vertexSet . vertices == Set.fromList

vertexCount :: AdjacencyMap a -> Int

algebraic-graphs Algebra.Graph.Acyclic.AdjacencyMap Algebra.Graph.AdjacencyMap

The number of vertices in a graph. Complexity: O(1) time.

vertexCount empty             ==  0
vertexCount (vertex x)        ==  1
vertexCount                   ==  length . vertexList
vertexCount x < vertexCount y ==> x < y

vertexList :: AdjacencyMap a -> [a]

algebraic-graphs Algebra.Graph.Acyclic.AdjacencyMap Algebra.Graph.AdjacencyMap

The sorted list of vertices of a given graph. Complexity: O(n) time and memory.

vertexList empty      == []
vertexList (vertex x) == [x]
vertexList . vertices == nub . sort

vertexSet :: AdjacencyMap a -> Set a

algebraic-graphs Algebra.Graph.Acyclic.AdjacencyMap Algebra.Graph.AdjacencyMap

The set of vertices of a given graph. Complexity: O(n) time and memory.

vertexSet empty      == Set.empty
vertexSet . vertex   == Set.singleton
vertexSet . vertices == Set.fromList

vertexCount :: AdjacencyIntMap -> Int

algebraic-graphs Algebra.Graph.AdjacencyIntMap

The number of vertices in a graph. Complexity: O(1) time.

vertexCount empty             ==  0
vertexCount (vertex x)        ==  1
vertexCount                   ==  length . vertexList
vertexCount x < vertexCount y ==> x < y

vertexIntSet :: AdjacencyIntMap -> IntSet

algebraic-graphs Algebra.Graph.AdjacencyIntMap

The set of vertices of a given graph. Complexity: O(n) time and memory.

vertexIntSet empty      == IntSet.empty
vertexIntSet . vertex   == IntSet.singleton
vertexIntSet . vertices == IntSet.fromList
vertexIntSet . clique   == IntSet.fromList

vertexList :: AdjacencyIntMap -> [Int]

algebraic-graphs Algebra.Graph.AdjacencyIntMap

The sorted list of vertices of a given graph. Complexity: O(n) time and memory.

vertexList empty      == []
vertexList (vertex x) == [x]
vertexList . vertices == nub . sort

vertexCount :: AdjacencyMap a b -> Int

algebraic-graphs Algebra.Graph.Bipartite.AdjacencyMap

The number of vertices in a graph. Complexity: O(1) time.

vertexCount empty      == 0
vertexCount (vertex x) == 1
vertexCount (edge x y) == 2
vertexCount x          == leftVertexCount x + rightVertexCount x