A wrapper around the types and functions from Data.Graph to make programming with them less painful. Also
implements some extra useful goodies such as successors
and sccGraph
, and improves the documentation of
the behaviour of some functions.
As it wraps Data.Graph, this module only supports directed graphs with unlabelled edges.
Incorporates code from the containers
package which is (c) The University of Glasgow 2002 and based
on code described in:
Lazy Depth-First Search and Linear Graph Algorithms in Haskell, by David King and John Launchbury
- type Edge i = (i, i)
- data Graph i v
- vertex :: Ord i => Graph i v -> i -> v
- fromListSimple :: Ord v => [(v, [v])] -> Graph v v
- fromList :: Ord i => [(i, v, [i])] -> Graph i v
- fromListLenient :: Ord i => [(i, v, [i])] -> Graph i v
- fromListBy :: Ord i => (v -> i) -> [(v, [i])] -> Graph i v
- fromVerticesEdges :: Ord i => [(i, v)] -> [Edge i] -> Graph i v
- toList :: Ord i => Graph i v -> [(i, v, [i])]
- vertices :: Graph i v -> [i]
- edges :: Graph i v -> [Edge i]
- successors :: Ord i => Graph i v -> i -> [i]
- outdegree :: Ord i => Graph i v -> i -> Int
- indegree :: Ord i => Graph i v -> i -> Int
- transpose :: Graph i v -> Graph i v
- reachableVertices :: Ord i => Graph i v -> i -> [i]
- hasPath :: Ord i => Graph i v -> i -> i -> Bool
- topologicalSort :: Graph i v -> [i]
- depthNumbering :: Ord i => Graph i v -> [i] -> Graph i (v, Maybe Int)
- data SCC i
- = AcyclicSCC i
- | CyclicSCC [i]
- stronglyConnectedComponents :: Graph i v -> [SCC i]
- sccGraph :: Ord i => Graph i v -> Graph (Set i) (Map i v)
- traverseWithKey :: Applicative t => (i -> a -> t b) -> Graph i a -> t (Graph i b)
Documentation
A directed graph
fromListSimple :: Ord v => [(v, [v])] -> Graph v vSource
Construct a Graph
where the vertex data double up as the indices.
Unlike Data.Graph.graphFromEdges
, vertex data that is listed as edges that are not actually themselves
present in the input list are reported as an error.
fromList :: Ord i => [(i, v, [i])] -> Graph i vSource
Construct a Graph
that contains the given vertex data, linked up according to the supplied index and edge list.
Unlike Data.Graph.graphFromEdges
, indexes in the edge list that do not correspond to the index of some item in the
input list are reported as an error.
fromListLenient :: Ord i => [(i, v, [i])] -> Graph i vSource
Construct a Graph
that contains the given vertex data, linked up according to the supplied index and edge list.
Like Data.Graph.graphFromEdges
, indexes in the edge list that do not correspond to the index of some item in the
input list are silently ignored.
fromListBy :: Ord i => (v -> i) -> [(v, [i])] -> Graph i vSource
Construct a Graph
that contains the given vertex data, linked up according to the supplied key extraction
function and edge list.
Unlike Data.Graph.graphFromEdges
, indexes in the edge list that do not correspond to the index of some item in the
input list are reported as an error.
fromVerticesEdges :: Ord i => [(i, v)] -> [Edge i] -> Graph i vSource
toList :: Ord i => Graph i v -> [(i, v, [i])]Source
Morally, the inverse of fromList
. The order of the elements in the output list is unspecified, as is the order of the edges
in each node's adjacency list. For this reason, toList . fromList
is not necessarily the identity function.
successors :: Ord i => Graph i v -> i -> [i]Source
Find the vertices we can reach from a vertex with the given indentity
transpose :: Graph i v -> Graph i vSource
The graph formed by flipping all the edges, so edges from i to j now go from j to i
reachableVertices :: Ord i => Graph i v -> i -> [i]Source
List all of the vertices reachable from the given starting point
hasPath :: Ord i => Graph i v -> i -> i -> BoolSource
Is the second vertex reachable by following edges from the first vertex?
It is worth sharing a partial application of hasPath
to the first vertex if you are testing for several
vertices being reachable from it.
topologicalSort :: Graph i v -> [i]Source
Topological sort of of the graph (http://en.wikipedia.org/wiki/Topological_sort). If the graph is acyclic, vertices will only appear in the list once all of those vertices with arrows to them have already appeared.
Vertex i precedes j in the output whenever j is reachable from i but not vice versa.
depthNumbering :: Ord i => Graph i v -> [i] -> Graph i (v, Maybe Int)Source
Number the vertices in the graph by how far away they are from the given roots. The roots themselves have depth 0,
and every subsequent link we traverse adds 1 to the depth. If a vertex is not reachable it will have a depth of Nothing
.
AcyclicSCC i | |
CyclicSCC [i] |
stronglyConnectedComponents :: Graph i v -> [SCC i]Source
Strongly connected components (http://en.wikipedia.org/wiki/Strongly_connected_component).
The SCCs are listed in a *reverse topological order*. That is to say, any edges *to* a node in the SCC originate either *from*:
1) Within the SCC itself (in the case of a CyclicSCC
only)
2) Or from a node in a SCC later on in the list
Vertex i strictly precedes j in the output whenever i is reachable from j but not vice versa. Vertex i occurs in the same SCC as j whenever both i is reachable from j and j is reachable from i.
sccGraph :: Ord i => Graph i v -> Graph (Set i) (Map i v)Source
The graph formed by the strongly connected components of the input graph. Each node in the resulting graph is indexed by the set of vertex indices from the input graph that it contains.
traverseWithKey :: Applicative t => (i -> a -> t b) -> Graph i a -> t (Graph i b)Source