Graaf  

Work with directed graphs in Rust.

Table of Contents

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

Installation

Add the following to your Cargo.toml:

[dependencies]
graaf = "0.75.3"

Digraph Types

Graaf provides three 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 eight 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.
• 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.

Basic Operations

Individual digraph types implement the basic operations.

• AddArcWeighted adds an arc to an arc-weighted digraph.
• AddArc adds an arc to an unweighted digraph.
• ArcWeight returns the weight of an arc.
• ArcsWeighted returns the arcs and their weights in a digraph.
• Arcs returns the arcs in a digraph.
• Converse returns the converse of a digraph.
• HasArc checks if an arc exists in a digraph.
• Indegree returns the indegree of a vertex.
• IsSimple checks if a digraph contains no loops or parallel arcs.
• Order returns the number of vertices.
• OutNeighborsWeighted returns the weighted out-neighbors of a vertex.
• OutNeighbors returns the out-neighbors of a vertex.
• Outdegree returns the outdegree of a vertex.
• RemoveArc removes an arc from a digraph.
• Size returns the number of arcs in a digraph.
• Vertices returns the vertices in a digraph.

Extended Operations

The extended traits derive their implementation from the basic operations.

• Complement returns the complement of a digraph.
• Degree returns the degree of a vertex.
• HasEdge checks if an edge exists in a digraph.
• IndegreeSequence returns the indegree sequence of a digraph.
• InNeighbors returns the in-neighbors of a vertex.
• IsBalanced checks if a digraph is balanced.
• IsComplete checks if a digraph is complete.
• IsIsolated checks if a vertex is isolated.
• IsOriented checks if a digraph is oriented.
• IsPendant checks if a vertex is a pendant.
• IsRegular checks if a digraph is regular.
• IsSemicomplete checks if a digraph is semicomplete.
• IsSpanningSubdigraph checks if a digraph is a spanning subdigraph.
• IsSubdigraph checks if a digraph is a subdigraph.
• IsSuperdigraph checks if a digraph is a superdigraph.
• IsSymmetric checks if a digraph is symmetric.
• IsTournament checks if a digraph is a tournament.
• IsWalk checks if a sequence of vertices is a walk in a digraph.
• OutdegreeSequence returns the outdegree sequence of a digraph.
• SemidegreeSequence returns the semidegree sequence of a digraph.
• Sinks returns the sinks in a digraph.
• Sources returns the sources in a digraph.

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.

These functions start from one or more source vertices and allow a custom step function, target predicate, distance array, breadth-first tree, and queue, 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_source_distances finds the shortest distances.
• single_source_predecessors finds the predecessors.
• single_pair_shortest_path finds the shortest path.

Depth-First Search (DFS)

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

• dfsa traverses the digraph.
• dfsa_predecessors finds the predecessors.
• acyclic_ordering generates an acyclic ordering.

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

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.

Breadth-First Tree

A breadth-first 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 breadth-first tree.

• bfs::single_source_predecessors
• bfs::predecessors
• dijkstra::single_source_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
• Full documentation
• Extensive property tests
• Complete unit test and benchmark coverage

Changelog

See CHANGELOG.md for a list of changes.

License

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