Data.Graph
 Portability non-portable (requires non-portable module ST) Stability experimental Maintainer libraries@haskell.org
 Contents External interface Graphs Building graphs Graph properties Algorithms
Description

A version of the graph algorithms described in:

Lazy Depth-First Search and Linear Graph Algorithms in Haskell, by David King and John Launchbury.

Synopsis
stronglyConnComp :: Ord key => [(node, key, [key])] -> [SCC node]
stronglyConnCompR :: Ord key => [(node, key, [key])] -> [SCC (node, key, [key])]
data SCC vertex
 = AcyclicSCC vertex | CyclicSCC [vertex]
flattenSCC :: SCC vertex -> [vertex]
flattenSCCs :: [SCC a] -> [a]
type Graph = Table [Vertex]
type Table a = Array Vertex a
type Bounds = (Vertex, Vertex)
type Edge = (Vertex, Vertex)
type Vertex = Int
graphFromEdges :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex)
graphFromEdges' :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]))
buildG :: Bounds -> [Edge] -> Graph
transposeG :: Graph -> Graph
vertices :: Graph -> [Vertex]
edges :: Graph -> [Edge]
outdegree :: Graph -> Table Int
indegree :: Graph -> Table Int
dfs :: Graph -> [Vertex] -> Forest Vertex
dff :: Graph -> Forest Vertex
topSort :: Graph -> [Vertex]
components :: Graph -> Forest Vertex
scc :: Graph -> Forest Vertex
bcc :: Graph -> Forest [Vertex]
reachable :: Graph -> Vertex -> [Vertex]
path :: Graph -> Vertex -> Vertex -> Bool
module Data.Tree
External interface
stronglyConnComp
 :: Ord key => [(node, key, [key])] The graph: a list of nodes uniquely identified by keys, with a list of keys of nodes this node has edges to. The out-list may contain keys that don't correspond to nodes of the graph; such edges are ignored. -> [SCC node] The strongly connected components of a directed graph, topologically sorted.
stronglyConnCompR
 :: Ord key => [(node, key, [key])] The graph: a list of nodes uniquely identified by keys, with a list of keys of nodes this node has edges to. The out-list may contain keys that don't correspond to nodes of the graph; such edges are ignored. -> [SCC (node, key, [key])] Topologically sorted The strongly connected components of a directed graph, topologically sorted. The function is the same as stronglyConnComp, except that all the information about each node retained. This interface is used when you expect to apply SCC to (some of) the result of SCC, so you don't want to lose the dependency information.
data SCC vertex
Strongly connected component.
Constructors
 AcyclicSCC vertex A single vertex that is not in any cycle. CyclicSCC [vertex] A maximal set of mutually reachable vertices.
flattenSCC :: SCC vertex -> [vertex]
The vertices of a strongly connected component.
flattenSCCs :: [SCC a] -> [a]
The vertices of a list of strongly connected components.
Graphs
type Graph = Table [Vertex]
Adjacency list representation of a graph, mapping each vertex to its list of successors.
type Table a = Array Vertex a
Table indexed by a contiguous set of vertices.
type Bounds = (Vertex, Vertex)
The bounds of a Table.
type Edge = (Vertex, Vertex)
An edge from the first vertex to the second.
type Vertex = Int
Abstract representation of vertices.
Building graphs
graphFromEdges :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex)
Build a graph from a list of nodes uniquely identified by keys, with a list of keys of nodes this node should have edges to. The out-list may contain keys that don't correspond to nodes of the graph; they are ignored.
graphFromEdges' :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]))
Identical to graphFromEdges, except that the return value does not include the function which maps keys to vertices. This version of graphFromEdges is for backwards compatibility.
buildG :: Bounds -> [Edge] -> Graph
Build a graph from a list of edges.
transposeG :: Graph -> Graph
The graph obtained by reversing all edges.
Graph properties
vertices :: Graph -> [Vertex]
All vertices of a graph.
edges :: Graph -> [Edge]
All edges of a graph.
outdegree :: Graph -> Table Int
A table of the count of edges from each node.
indegree :: Graph -> Table Int
A table of the count of edges into each node.
Algorithms
dfs :: Graph -> [Vertex] -> Forest Vertex
A spanning forest of the part of the graph reachable from the listed vertices, obtained from a depth-first search of the graph starting at each of the listed vertices in order.
dff :: Graph -> Forest Vertex
A spanning forest of the graph, obtained from a depth-first search of the graph starting from each vertex in an unspecified order.
topSort :: Graph -> [Vertex]
A topological sort of the graph. The order is partially specified by the condition that a vertex i precedes j whenever j is reachable from i but not vice versa.
components :: Graph -> Forest Vertex
The connected components of a graph. Two vertices are connected if there is a path between them, traversing edges in either direction.
scc :: Graph -> Forest Vertex
The strongly connected components of a graph.
bcc :: Graph -> Forest [Vertex]
The biconnected components of a graph. An undirected graph is biconnected if the deletion of any vertex leaves it connected.
reachable :: Graph -> Vertex -> [Vertex]
A list of vertices reachable from a given vertex.
path :: Graph -> Vertex -> Vertex -> Bool
Is the second vertex reachable from the first?
module Data.Tree