Graaf  

Rust-powered directed graphs.

Table of Contents

• Installation
• Digraph Types
• Creating Digraphs
• Operations
• Algorithms
  • Bellman-Ford-Moore
  • Breadth-First Search (BFS)
  • Depth-First Search (DFS)
  • Dijkstra
  • Floyd-Warshall
  • Tarjan
  • Types
    • Predecessor Tree
    • Distance Matrix
• Naming Conventions
• Project Goals
• Changelog
• License
• Contact
• Links

Installation

Add the following to your Cargo.toml:

[dependencies]
graaf = "0.80.0"

Digraph Types

Graaf provides representations of directed graphs.

• adjacency_list represents unweighted sparse digraphs.
• adjacency_matrix represents unweighted dense digraphs.
• adjacency_list_weighted represents arc-weighted sparse digraphs.

These types eagerly implement digraph operations and digraph algorithms.

Creating Digraphs

The gen module provides digraph 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 with no arcs.
• ErdosRenyi generates a random digraph.
• Path generates a path digraph.
• RandomTournament generates a random tournament.
• Star generates a star digraph.

Operations

The op module provides digraph operation traits. The digraph types implement these traits. One can implement these traits for custom digraph types. Operations form the foundation for algorithms.

• AddArcWeighted adds an arc to an arc-weighted digraph.
• AddArc adds an arc to an unweighted digraph.
• ArcWeight returns an arc's weight.
• ArcsWeighted returns a digraph's arcs and their weights.
• Arcs returns a digraph's arcs.
• Complement returns a digraph's complement.
• Converse returns a digraph's converse.
• DegreeSequence returns a digraph's degree sequence.
• Degree returns a vertex's degree.
• 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 returns a vertex's in-neighbors.
• IndegreeSequence returns a digraph's indegree sequence.
• Indegree returns 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 does not contain loops or parallel arcs.
• IsSpanningSubdigraph checks whether a digraph is a spanning subdigraph.
• 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 returns a vertex's out-neighbors and their weights.
• OutNeighbors returns a vertex's out-neighbors.
• OutdegreeSequence returns a digraph's outdegree sequence.
• Outdegree returns a vertex's outdegree.
• RemoveArc removes an arc from a digraph.
• SemidegreeSequence returns a digraph's semidegree sequence.
• Sinks returns a digraph's sinks.
• Size returns the number of arcs in a digraph.
• Sources returns a digraph's sources.
• Vertices returns a digraph's vertices.

Algorithms

The algo module provides digraph algorithms.

Bellman-Ford-Moore

The Bellman-Ford-Moore algorithm finds the shortest paths in an arc-weighted digraph with negative weights.

• single_source_distances finds the shortest distances.

Breadth-First Search (BFS)

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

• bfs::Bfs iterates over the vertices.
• bfs_depth::Bfs::distances finds the distances.
• bfs_depth::Bfs iterates over the vertices and their depths.
• bfs_successors::Bfs::predecessors finds the predecessors.
• bfs_successors::Bfs::shortest_path finds the shortest path.
• bfs_successors::Bfs iterates over the vertices and their successors.

Depth-First Search (DFS)

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

• dfs::Dfs iterates over the vertices.
• dfs_depth::Dfs iterates over the vertices and their depths.

Dijkstra

Dijkstra's algorithm finds the shortest paths in an arc-weighted digraph.

These functions start from one or more source vertices and allow a custom step function, target predicate, distance array, and heap, where applicable.

• distances finds the shortest distances.
• predecessors finds the predecessors.
• shortest_path finds the shortest path.

These functions start from one source vertex.

• single_pair_shortest_path finds the shortest path.
• single_source_distances finds the shortest distances.
• single_source_predecessors finds the predecessors.

Floyd-Warshall

The Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices in an arc-weighted digraph.

• distances finds the shortest distances.

Tarjan

Tarjan's algorithm finds the strongly connected components in a digraph.

• strongly_connected_components finds the strongly connected components.

Types

These types are produced by the algorithms.

Predecessor Tree

A predecessor tree is the result of a breadth-first search.

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

These functions produce a predecessor tree.

• bfs_successors::Bfs::predecessors
• dijkstra::predecessors

Distance Matrix

A distance matrix contains the shortest distances between all pairs of vertices in a digraph.

• center finds the center of the digraph.
• diameter finds the diameter of the digraph.
• eccentricities returns the eccentricities of the vertices.
• is_connected checks if the digraph is connected.
• periphery finds the periphery of the digraph.

Naming Conventions

• s denotes a source vertex.
• t denotes a target vertex.
• u denotes a tail vertex or the first vertex in scope.
• v denotes a head vertex or the second vertex in scope.
• w denotes the weight of an arc.
• x denotes a tail vertex or the third vertex in scope.
• y denotes a head vertex or the fourth vertex in scope.

Project Goals

• A flexible API for digraph operations
• A comprehensive set of algorithms
• Generators for common digraphs
• Competitive performance
• Complete documentation
• Extensive property tests
• Complete unit test coverage

Changelog

See CHANGELOG.md for a list of changes.

License

Licensed under Apache License, Version 2.0 or MIT license at your option.

Contact

Feel free to reach out with questions or suggestions.

• Email
• GitHub

Links

• Crates.io
• Docs.rs
• Coveralls