GraphSCC-1.0: Tarjan's algorithm for computing the strongly connected components of a graph.

Data.Graph.SCC

Synopsis

# Documentation

scc :: Graph -> ([(Int, [Vertex])], Vertex -> Int)Source

Computes the strongly connected components (SCCs) of the graph in O(vertices) time. The resulting tuple contains: * A (reversed) topologically sorted list of SCCs. Each SCCs is assigned a unique identifier of type `Int`. * An O(1) mapping from vertices in the original graph to the identifier of their SCC. This mapping will raise an out of bounds exception if it is applied to integers that do not correspond to vertices in the input graph.

This function assumes that the adjacency lists in the original graph mention only nodes that are in the graph. Violating this assumption will result in out of bounds array exception.

sccList :: Graph -> [SCC Vertex]Source

Compute the list of strongly connected components of a graph. The components are topologically sorted: if v1 in C1 points to v2 in C2, then C2 will come before C1 in the list.

sccListR :: Graph -> [SCC (Vertex, [Vertex])]Source

Compute the list of strongly connected components of a graph. Each component contains the adjecency information from the original graph. The components are topologically sorted: if v1 in C1 points to v2 in C2, then C2 will come before C1 in the list.

sccGraph :: Graph -> [(SCC Int, Int, [Int])]Source

Quotient a graph with the relation that relates vertices that belong to the same SCC. The vertices in the new graph are the SCCs of the old graph, and there is an edge between two components, if there is an edge between any of their vertices. The entries in the resulting list are in reversed-topologically sorted: if v1 in C1 points to v2 in C2, then C1 will come before C2 in the list.

stronglyConnComp :: Ord key => [(node, key, [key])] -> [SCC node]Source

stronglyConnCompR :: Ord key => [(node, key, [key])] -> [SCC (node, key, [key])]Source