Copyright | (c) The University of Glasgow 2002 |
---|---|

License | BSD-style (see the file libraries/base/LICENSE) |

Maintainer | libraries@haskell.org |

Stability | experimental |

Portability | portable |

Safe Haskell | Trustworthy |

Language | Haskell98 |

A version of the graph algorithms described in:

*Structuring Depth-First Search Algorithms in Haskell*, by David King and John Launchbury.

:: 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.

:: 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.

Strongly connected component.

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.

type Graph = Table [Vertex] Source

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

type Table a = Array Vertex a Source

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.

Abstract representation of vertices.

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.

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.

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

© The University of Glasgow and others

Licensed under a BSD-style license (see top of the page).

https://downloads.haskell.org/~ghc/7.10.3/docs/html/libraries/containers-0.5.6.2/Data-Graph.html