Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org
Safe Haskell	Trustworthy

Data.Graph

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

External interface

stronglyConnComp Source

Arguments

:: 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 Source

Arguments

:: 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 Source

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]Source

The vertices of a strongly connected component.

flattenSCCs :: [SCC a] -> [a]Source

The vertices of a list of strongly connected components.

Graphs

type Graph = Table [Vertex]Source

Adjacency list representation of a graph, mapping each vertex to its list of successors.

type Table a = Array Vertex aSource

Table indexed by a contiguous set of vertices.

type Bounds = (Vertex, Vertex)Source

The bounds of a Table.

type Edge = (Vertex, Vertex)Source

An edge from the first vertex to the second.

type Vertex = Int Source

Abstract representation of vertices.

Building graphs

graphFromEdges :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex)Source

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]))Source

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 Source

Build a graph from a list of edges.

transposeG :: Graph -> Graph Source

The graph obtained by reversing all edges.

Graph properties

vertices :: Graph -> [Vertex]Source

All vertices of a graph.

edges :: Graph -> [Edge]Source

All edges of a graph.

outdegree :: Graph -> Table Int Source

A table of the count of edges from each node.

indegree :: Graph -> Table Int Source

A table of the count of edges into each node.

Algorithms

dfs :: Graph -> [Vertex] -> Forest Vertex Source

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 Source

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]Source

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 Source

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 Source

The strongly connected components of a graph.

bcc :: Graph -> Forest [Vertex]Source

The biconnected components of a graph. An undirected graph is biconnected if the deletion of any vertex leaves it connected.

reachable :: Graph -> Vertex -> [Vertex]Source

A list of vertices reachable from a given vertex.

path :: Graph -> Vertex -> Vertex -> Bool Source

Is the second vertex reachable from the first?

module Data.Tree