graphite-0.9.3.0: Graphs and networks library

Data.Graph.Types

Contents

Synopsis

# Documentation

class Graph g where Source #

Types that behave like graphs | | The main Graph instances are UGraph and DGraph. The functions in this class should be used for algorithms that are graph-directionality agnostic, otherwise use the more specific ones in UGraph and DGraph

Minimal complete definition

Methods

empty :: Hashable v => g v e Source #

The Empty (order-zero) graph with no vertices and no edges

order :: g v e -> Int Source #

Retrieve the order of a graph | The order of a graph is its number of vertices

size :: (Hashable v, Eq v) => g v e -> Int Source #

Retrieve the size of a graph | The size of a graph is its number of edges

density :: (Hashable v, Eq v) => g v e -> Double Source #

Density of a graph | The ratio of the number of existing edges in the graph to the number of | posible edges

vertices :: g v e -> [v] Source #

Retrieve the vertices of a graph

edgeTriples :: (Hashable v, Eq v) => g v e -> [(v, v, e)] Source #

Retrieve the edges of a graph

edgePairs :: (Hashable v, Eq v) => g v e -> [(v, v)] Source #

Retrieve the edges of a graph, ignoring its attributes

containsVertex :: (Hashable v, Eq v) => g v e -> v -> Bool Source #

Tell if a vertex exists in the graph

areAdjacent :: (Hashable v, Eq v) => g v e -> v -> v -> Bool Source #

Tell if two vertices are adjacent

adjacentVertices :: (Hashable v, Eq v) => g v e -> v -> [v] Source #

Retrieve the adjacent vertices of a vertex

adjacentVertices' :: (Hashable v, Eq v) => g v e -> v -> [(v, v, e)] Source #

Same as adjacentVertices but gives back the connecting edges

reachableAdjacentVertices :: (Hashable v, Eq v) => g v e -> v -> [v] Source #

Same as adjacentVertices but gives back only those vertices for which | the connecting edge allows the vertex to be reached. | | For an undirected graph this is equivalent to adjacentVertices, but | for the case of a directed graph, the directed arcs will constrain the | reachability of the adjacent vertices.

reachableAdjacentVertices' :: (Hashable v, Eq v) => g v e -> v -> [(v, v, e)] Source #

Same as reachableAdjacentVertices but gives back the connecting edges

vertexDegree :: (Hashable v, Eq v) => g v e -> v -> Int Source #

Total number of incident edges of a vertex

degrees :: (Hashable v, Eq v) => g v e -> [Int] Source #

Degrees of a all the vertices in a graph

maxDegree :: (Hashable v, Eq v) => g v e -> Int Source #

Maximum degree of a graph

minDegree :: (Hashable v, Eq v) => g v e -> Int Source #

Minimum degree of a graph

avgDegree :: (Hashable v, Eq v) => g v e -> Double Source #

Average degree of a graph

insertVertex :: (Hashable v, Eq v) => v -> g v e -> g v e Source #

Insert a vertex into a graph | If the graph already contains the vertex leave the graph untouched

insertVertices :: (Hashable v, Eq v) => [v] -> g v e -> g v e Source #

Insert a many vertices into a graph | New vertices are inserted and already contained vertices are left | untouched

containsEdgePair :: (Hashable v, Eq v) => g v e -> (v, v) -> Bool Source #

Tell if an edge exists in the graph

incidentEdgeTriples :: (Hashable v, Eq v) => g v e -> v -> [(v, v, e)] Source #

Retrieve the incident edges of a vertex

incidentEdgePairs :: (Hashable v, Eq v) => g v e -> v -> [(v, v)] Source #

Retrieve the incident edges of a vertex, ignoring its attributes

edgeTriple :: (Hashable v, Eq v) => g v e -> v -> v -> Maybe (v, v, e) Source #

Get the edge between to vertices if it exists

insertEdgeTriple :: (Hashable v, Eq v) => (v, v, e) -> g v e -> g v e Source #

Insert an edge into a graph | The involved vertices are inserted if don't exist. If the graph already | contains the edge, its attribute is updated

insertEdgeTriples :: (Hashable v, Eq v) => [(v, v, e)] -> g v e -> g v e Source #

Same as insertEdgeTriple but for multiple edges

insertEdgePair :: (Hashable v, Eq v) => (v, v) -> g v () -> g v () Source #

Same as insertEdgeTriple but insert edge pairs in graphs with | attributeless edges

insertEdgePairs :: (Hashable v, Eq v) => [(v, v)] -> g v () -> g v () Source #

Same as insertEdgePair for multiple edges

removeVertex :: (Hashable v, Eq v) => v -> g v e -> g v e Source #

Remove a vertex from a graph if present | Every edge incident to this vertex is also removed

removeVertices :: (Hashable v, Eq v) => [v] -> g v e -> g v e Source #

Same as removeVertex but for multiple vertices

removeEdgePair :: (Hashable v, Eq v) => (v, v) -> g v e -> g v e Source #

Remove an edge from a graph if present | The involved vertices are left untouched

removeEdgePairs :: (Hashable v, Eq v) => [(v, v)] -> g v e -> g v e Source #

Same as removeEdgePair but for multple edges

removeEdgePairAndVertices :: (Hashable v, Eq v) => (v, v) -> g v e -> g v e Source #

Remove the edge from a graph if present | The involved vertices are also removed

isSimple :: (Hashable v, Eq v) => g v e -> Bool Source #

Tell if a graph is simple | A graph is simple if it has no loops

union :: g v e -> g v e -> g v e Source #

Union of two graphs

intersection :: g v e -> g v e -> g v e Source #

Intersection of two graphs

join :: g v e -> g v e -> g v e Source #

Join two graphs | | The join of two graphs G1 and G2 is a new graph where each vertex of | G1 has an edge to all the vertices of G2

toList :: (Hashable v, Eq v) => g v e -> [(v, [(v, e)])] Source #

Convert a graph to an adjacency list with edge attributes in e

fromList :: (Hashable v, Eq v) => [(v, [(v, e)])] -> g v e Source #

Construct a graph from an adjacency list with edge attributes in e

toAdjacencyMatrix :: g v e -> [[Int]] Source #

Get the adjacency binary matrix representation of a grah

fromAdjacencyMatrix :: [[Int]] -> Maybe (g Int ()) Source #

Generate a graph of Int vertices from an adjacency | square binary matrix

Instances

class IsEdge e where Source #

Types that represent edges | | The main IsEdge instances are Edge for undirected edges and Arc for directed edges.

Minimal complete definition

Methods

originVertex :: e v a -> v Source #

Retrieve the origin vertex of the edge

destinationVertex :: e v a -> v Source #

Retrieve the destination vertex of the edge

attribute :: e v a -> a Source #

Retrieve the attribute of the edge

toPair :: e v a -> (v, v) Source #

Convert an edge to a pair discarding its attribute

fromPair :: (v, v) -> e v () Source #

Convert a pair to an edge, where it's attribute is unit

toTriple :: e v a -> (v, v, a) Source #

Convert an edge to a triple, where the 3rd element it's the edge | attribute

fromTriple :: (v, v, a) -> e v a Source #

Convert a triple to an edge

isLoop :: Eq v => e v a -> Bool Source #

Tell if an edge is a loop | An edge forms a loop if both of its ends point to the same vertex

Instances

 Source # MethodsoriginVertex :: Arc v a -> v Source #destinationVertex :: Arc v a -> v Source #attribute :: Arc v a -> a Source #toPair :: Arc v a -> (v, v) Source #fromPair :: (v, v) -> Arc v () Source #toTriple :: Arc v a -> (v, v, a) Source #fromTriple :: (v, v, a) -> Arc v a Source #isLoop :: Eq v => Arc v a -> Bool Source # Source # MethodsoriginVertex :: Edge v a -> v Source #destinationVertex :: Edge v a -> v Source #attribute :: Edge v a -> a Source #toPair :: Edge v a -> (v, v) Source #fromPair :: (v, v) -> Edge v () Source #toTriple :: Edge v a -> (v, v, a) Source #fromTriple :: (v, v, a) -> Edge v a Source #isLoop :: Eq v => Edge v a -> Bool Source #

data Edge v e Source #

Undirected Edge with attribute of type e between to Vertices of type v

Constructors

 Edge v v e

Instances

 Source # MethodsoriginVertex :: Edge v a -> v Source #destinationVertex :: Edge v a -> v Source #attribute :: Edge v a -> a Source #toPair :: Edge v a -> (v, v) Source #fromPair :: (v, v) -> Edge v () Source #toTriple :: Edge v a -> (v, v, a) Source #fromTriple :: (v, v, a) -> Edge v a Source #isLoop :: Eq v => Edge v a -> Bool Source # Functor (Edge v) Source # Methodsfmap :: (a -> b) -> Edge v a -> Edge v b #(<$) :: a -> Edge v b -> Edge v a # (Eq v, Eq a) => Eq (Edge v a) Source # Two Edges are equal if they point to the same vertices, regardless of the | direction Methods(==) :: Edge v a -> Edge v a -> Bool #(/=) :: Edge v a -> Edge v a -> Bool # (Ord e, Ord v) => Ord (Edge v e) Source # Methodscompare :: Edge v e -> Edge v e -> Ordering #(<) :: Edge v e -> Edge v e -> Bool #(<=) :: Edge v e -> Edge v e -> Bool #(>) :: Edge v e -> Edge v e -> Bool #(>=) :: Edge v e -> Edge v e -> Bool #max :: Edge v e -> Edge v e -> Edge v e #min :: Edge v e -> Edge v e -> Edge v e # (Read e, Read v) => Read (Edge v e) Source # MethodsreadsPrec :: Int -> ReadS (Edge v e) #readList :: ReadS [Edge v e] #readPrec :: ReadPrec (Edge v e) #readListPrec :: ReadPrec [Edge v e] # (Show e, Show v) => Show (Edge v e) Source # MethodsshowsPrec :: Int -> Edge v e -> ShowS #show :: Edge v e -> String #showList :: [Edge v e] -> ShowS # Generic (Edge v e) Source # Associated Typestype Rep (Edge v e) :: * -> * # Methodsfrom :: Edge v e -> Rep (Edge v e) x #to :: Rep (Edge v e) x -> Edge v e # (Arbitrary v, Arbitrary e, Num v, Ord v) => Arbitrary (Edge v e) Source # Methodsarbitrary :: Gen (Edge v e) #shrink :: Edge v e -> [Edge v e] # (NFData v, NFData e) => NFData (Edge v e) Source # Methodsrnf :: Edge v e -> () # type Rep (Edge v e) Source # type Rep (Edge v e) = D1 (MetaData "Edge" "Data.Graph.Types" "graphite-0.9.3.0-LlSq1bz2zFSFNwvGP6MMQ3" False) (C1 (MetaCons "Edge" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 v)) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 v)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e))))) data Arc v e Source # Directed Arc with attribute of type e between to Vertices of type v Constructors  Arc v v e Instances  Source # MethodsoriginVertex :: Arc v a -> v Source #destinationVertex :: Arc v a -> v Source #attribute :: Arc v a -> a Source #toPair :: Arc v a -> (v, v) Source #fromPair :: (v, v) -> Arc v () Source #toTriple :: Arc v a -> (v, v, a) Source #fromTriple :: (v, v, a) -> Arc v a Source #isLoop :: Eq v => Arc v a -> Bool Source # Functor (Arc v) Source # Methodsfmap :: (a -> b) -> Arc v a -> Arc v b #(<$) :: a -> Arc v b -> Arc v a # (Eq v, Eq a) => Eq (Arc v a) Source # Two Arcs are equal if they point to the same vertices, and the directions | are the same Methods(==) :: Arc v a -> Arc v a -> Bool #(/=) :: Arc v a -> Arc v a -> Bool # (Ord e, Ord v) => Ord (Arc v e) Source # Methodscompare :: Arc v e -> Arc v e -> Ordering #(<) :: Arc v e -> Arc v e -> Bool #(<=) :: Arc v e -> Arc v e -> Bool #(>) :: Arc v e -> Arc v e -> Bool #(>=) :: Arc v e -> Arc v e -> Bool #max :: Arc v e -> Arc v e -> Arc v e #min :: Arc v e -> Arc v e -> Arc v e # (Read e, Read v) => Read (Arc v e) Source # MethodsreadsPrec :: Int -> ReadS (Arc v e) #readList :: ReadS [Arc v e] #readPrec :: ReadPrec (Arc v e) #readListPrec :: ReadPrec [Arc v e] # (Show e, Show v) => Show (Arc v e) Source # MethodsshowsPrec :: Int -> Arc v e -> ShowS #show :: Arc v e -> String #showList :: [Arc v e] -> ShowS # Generic (Arc v e) Source # Associated Typestype Rep (Arc v e) :: * -> * # Methodsfrom :: Arc v e -> Rep (Arc v e) x #to :: Rep (Arc v e) x -> Arc v e # (Arbitrary v, Arbitrary e, Num v, Ord v) => Arbitrary (Arc v e) Source # Methodsarbitrary :: Gen (Arc v e) #shrink :: Arc v e -> [Arc v e] # (NFData v, NFData e) => NFData (Arc v e) Source # Methodsrnf :: Arc v e -> () # type Rep (Arc v e) Source # type Rep (Arc v e) = D1 (MetaData "Arc" "Data.Graph.Types" "graphite-0.9.3.0-LlSq1bz2zFSFNwvGP6MMQ3" False) (C1 (MetaCons "Arc" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 v)) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 v)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)))))

(<->) :: Hashable v => v -> v -> Edge v () Source #

Construct an attributeless undirected Edge between two vertices

(-->) :: Hashable v => v -> v -> Arc v () Source #

Construct an attributeless directed Arc between two vertices

class Weighted e where Source #

Weighted Edge attributes

Minimal complete definition

weight

Methods

weight :: e -> Double Source #

Instances

 Source # Methods Source # Methods Source # Methods Source # Methodsweight :: (Double, String) -> Double Source #

class Labeled e where Source #

Labeled Edge attributes

Minimal complete definition

label

Methods

label :: e -> String Source #

Instances

 Source # Methods Source # Methodslabel :: (Double, String) -> String Source #

arbitraryEdge :: (Arbitrary v, Arbitrary e, Ord v, Num v) => (v -> v -> e -> edge) -> Gen edge Source #

Edges generator

# Triples convenience functions

tripleToPair :: (a, b, c) -> (a, b) Source #

Convert a triple to a pair by ignoring the third element

pairToTriple :: (a, b) -> (a, b, ()) Source #

Convert a pair to a triple where the 3rd element is unit

tripleOriginVertex :: (v, v, e) -> v Source #

Get the origin vertex from an edge triple

tripleDestVertex :: (v, v, e) -> v Source #

Get the destination vertex from an edge triple

tripleAttribute :: (v, v, e) -> e Source #

Get the attribute from an edge triple