Crate graaf

Graaf

Rust-powered directed graphs.

Table of Contents

• Representations
• Generators
• Operations
• Algorithms
  • Bellman-Ford-Moore
  • Breadth-First Search
  • Depth-First Search
  • Dijkstra
  • Distance Matrix
  • Floyd-Warshall
  • Johnson’s Circuit-Finding Algorithm
  • Predecessor Tree
  • Tarjan

Representations

Arc-Weighted Sparse Digraphs

• AdjacencyListWeighted represents a digraph as a vector of maps.

Unweighted Dense Digraphs

• AdjacencyMatrix represents a digraph as a matrix using a bit vector.

Unweighted Sparse Digraphs

• AdjacencyList represents a digraph as a vector of sets.
• AdjacencyMap represents a digraph as a map of sets.
• EdgeList represents a digraph as a vector of tuples.

Generators

• Biclique generates a complete bipartite digraph.
• Circuit generates a circuit digraph.
• Complete generates a complete digraph.
• Cycle generates a bidirectional circuit.
• Empty generates a digraph without arcs.
• ErdosRenyi generates a random digraph.
• GrowingNetwork generates a growing network.
• Path generates a path digraph.
• RandomTournament generates a random tournament.
• Star generates a star digraph.
• Wheel generates a wheel digraph.

Operations

• AddArcWeighted adds an arc to an arc-weighted digraph.
• AddArc adds an arc to an unweighted digraph.
• ArcWeight returns an arc’s weight.
• ArcsWeighted iterates over a digraph’s weighted arcs.
• Arcs iterates over a digraph’s arcs.
• Complement returns a digraph’s complement.
• Converse returns a digraph’s converse.
• DegreeSequence iterates over a digraph’s degrees.
• Degree returns a vertex’s degree.
• FilterVertices filters a digraph’s vertices.
• HasArc checks whether a digraph contains an arc.
• HasEdge checks whether a digraph contains an edge.
• HasWalk checks whether a digraph contains a walk.
• InNeighbors iterates over a vertex’s in-neighbors.
• IndegreeSequence iterates over a digraph’s indegrees.
• Indegree a vertex’s indegree.
• IsBalanced checks whether a digraph is balanced.
• IsComplete checks whether a digraph is complete.
• IsIsolated checks whether a vertex is isolated.
• IsOriented checks whether a digraph is oriented.
• IsPendant checks whether a vertex is a pendant.
• IsRegular checks whether a digraph is regular.
• IsSemicomplete checks whether a digraph is semicomplete.
• IsSimple checks whether a digraph is simple.
• IsSpanningSubdigraph checks whether a digraph spans a superdigraph.
• IsSubdigraph checks whether a digraph is a subdigraph.
• IsSuperdigraph checks whether a digraph is a superdigraph.
• IsSymmetric checks whether a digraph is symmetric.
• IsTournament checks whether a digraph is a tournament.
• Order returns the number of vertices in a digraph.
• OutNeighborsWeighted iterates over a vertex’s weighted out-neighbors.
• OutNeighbors iterates over a vertex’s out-neighbors.
• OutdegreeSequence iterates over a digraph’s outdegrees.
• Outdegree returns a vertex’s outdegree.
• RemoveArc removes an arc from a digraph.
• SemidegreeSequence iterates over a digraph’s semidegrees.
• Sinks iterates over a digraph’s sinks.
• Size returns the number of arcs in a digraph.
• Sources iterates over a digraph’s sources.
• Union returns the union of two digraphs.
• Vertices iterates over a digraph’s vertices.

Algorithms

Bellman-Ford-Moore

Find the shortest distances from a source vertex to all other vertices in an arc-weighted digraph with negative weights.

• BellmanFordMoore::distances finds the shortest distances.

Breadth-First Search

A breadth-first search explores an unweighted digraph’s vertices in order of their distance from a source.

• Bfs iterates the vertices.
• BfsDist iterates the vertices and their distance from the source.
• BfsPred iterates the vertices and their predecessors.
• BfsDist::distances finds the shortest distances.
• BfsPred::cycles returns the cycles along the shortest path.
• BfsPred::predecessors finds the predecessors.
• BfsPred::shortest_path finds the shortest path.

Depth-First Search

A depth-first search explores an unweighted digraph’s vertices in order of their distance from a source.

• Dfs iterates the vertices.
• DfsDist iterates the vertices and their distance from the source.
• DfsPred iterates the vertices and their predecessors.
• DfsPred::predecessors finds the predecessors.

Dijkstra

Dijkstra’s algorithm finds the shortest paths from one or more source vertices in an arc-weighted digraph.

• Dijkstra iterates the vertices.
• DijkstraDist iterates the vertices and their distance from the source.
• DijkstraPred iterates the vertices and their predecessors.
• DijkstraDist::distances finds the shortest distances.
• DijkstraPred::predecessors finds the predecessors.
• DijkstraPred::shortest_path finds the shortest path.

Distance Matrix

A DistanceMatrix contains the shortest distances between all vertex pairs in a digraph.

• DistanceMatrix::center finds the digraph’s center.
• DistanceMatrix::diameter finds the digraph’s diameter.
• DistanceMatrix::eccentricities the vertices’ eccentricities.
• DistanceMatrix::is_connected checks the digraph’s connectedness.
• DistanceMatrix::periphery finds the digraph’s periphery.

Floyd-Warshall

The Floyd-Warshall algorithm finds the distance between each vertex pair in an arc-weighted digraph.

• FloydWarshall::distances finds the shortest distances.

Johnson’s Circuit-Finding Algorithm

Johnson’s circuit-finding algorithm finds all circuits in a digraph.

• Johnson75::circuits finds all circuits.

Predecessor Tree

A PredecessorTree is the result of a search and contains the vertices’ predecessors.

• PredecessorTree::search finds a vertex by value.
• PredecessorTree::search_by finds a vertex by predicate.

Tarjan

Tarjan’s algorithm finds strongly connected components in a digraph.

• Tarjan::components finds strongly connected components.

Re-exports

• pub use repr::AdjacencyList;
• pub use repr::AdjacencyListWeighted;
• pub use repr::AdjacencyMap;
• pub use repr::AdjacencyMatrix;
• pub use repr::EdgeList;
• pub use op::AddArc;
• pub use op::AddArcWeighted;
• pub use op::ArcWeight;
• pub use op::Arcs;
• pub use op::ArcsWeighted;
• pub use op::Complement;
• pub use op::Converse;
• pub use op::Degree;
• pub use op::DegreeSequence;
• pub use op::FilterVertices;
• pub use op::HasArc;
• pub use op::HasEdge;
• pub use op::HasWalk;
• pub use op::InNeighbors;
• pub use op::Indegree;
• pub use op::IndegreeSequence;
• pub use op::IsBalanced;
• pub use op::IsComplete;
• pub use op::IsIsolated;
• pub use op::IsOriented;
• pub use op::IsPendant;
• pub use op::IsRegular;
• pub use op::IsSemicomplete;
• pub use op::IsSimple;
• pub use op::IsSpanningSubdigraph;
• pub use op::IsSubdigraph;
• pub use op::IsSuperdigraph;
• pub use op::IsSymmetric;
• pub use op::IsTournament;
• pub use op::Order;
• pub use op::OutNeighbors;
• pub use op::OutNeighborsWeighted;
• pub use op::Outdegree;
• pub use op::OutdegreeSequence;
• pub use op::RemoveArc;
• pub use op::SemidegreeSequence;
• pub use op::Sinks;
• pub use op::Size;
• pub use op::Sources;
• pub use op::Union;
• pub use op::Vertices;
• pub use gen::Biclique;
• pub use gen::Circuit;
• pub use gen::Complete;
• pub use gen::Cycle;
• pub use gen::Empty;
• pub use gen::ErdosRenyi;
• pub use gen::GrowingNetwork;
• pub use gen::Path;
• pub use gen::RandomTournament;
• pub use gen::Star;
• pub use gen::Wheel;
• pub use algo::bellman_ford_moore::BellmanFordMoore;
• pub use algo::bfs::Bfs;
• pub use algo::bfs_dist::BfsDist;
• pub use algo::bfs_pred::BfsPred;
• pub use algo::dfs::Dfs;
• pub use algo::dfs_dist::DfsDist;
• pub use algo::dfs_pred::DfsPred;
• pub use algo::dijkstra::Dijkstra;
• pub use algo::dijkstra_dist::DijkstraDist;
• pub use algo::dijkstra_pred::DijkstraPred;
• pub use algo::distance_matrix::DistanceMatrix;
• pub use algo::floyd_warshall::FloydWarshall;
• pub use algo::johnson_75::Johnson75;
• pub use algo::predecessor_tree::PredecessorTree;
• pub use algo::tarjan::Tarjan;

Modules

• algo
  Digraph algorithms
• gen
  Generate parameterized and random digraphs.
• op
  Operations on digraphs
• repr
  Digraph representations.

Macros

• test_unweighted
  Common tests for unweighted digraphs.