1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
//! `petgraph` is a graph data structure library.
//!
//! Graphs are collections of nodes, and edges between nodes. `petgraph`
//! provides several [graph types](index.html#graph-types) (each differing in the
//! tradeoffs taken in their internal representation),
//! [algorithms](./algo/index.html#functions) on those graphs, and functionality to
//! [output graphs](./dot/struct.Dot.html) in
//! [`graphviz`](https://www.graphviz.org/) format. Both nodes and edges
//! can have arbitrary associated data, and edges may be either directed or undirected.
//!
//! # Example
//!
//! ```rust
//! use petgraph::graph::{NodeIndex, UnGraph};
//! use petgraph::algo::{dijkstra, min_spanning_tree};
//! use petgraph::data::FromElements;
//! use petgraph::dot::{Dot, Config};
//!
//! // Create an undirected graph with `i32` nodes and edges with `()` associated data.
//! let g = UnGraph::<i32, ()>::from_edges(&[
//!     (1, 2), (2, 3), (3, 4),
//!     (1, 4)]);
//!
//! // Find the shortest path from `1` to `4` using `1` as the cost for every edge.
//! let node_map = dijkstra(&g, 1.into(), Some(4.into()), |_| 1);
//! assert_eq!(&1i32, node_map.get(&NodeIndex::new(4)).unwrap());
//!
//! // Get the minimum spanning tree of the graph as a new graph, and check that
//! // one edge was trimmed.
//! let mst = UnGraph::<_, _>::from_elements(min_spanning_tree(&g));
//! assert_eq!(g.raw_edges().len() - 1, mst.raw_edges().len());
//!
//! // Output the tree to `graphviz` `DOT` format
//! println!("{:?}", Dot::with_config(&mst, &[Config::EdgeNoLabel]));
//! // graph {
//! //     0 [label="\"0\""]
//! //     1 [label="\"0\""]
//! //     2 [label="\"0\""]
//! //     3 [label="\"0\""]
//! //     1 -- 2
//! //     3 -- 4
//! //     2 -- 3
//! // }
//! ```
//!
//! # Graph types
//!
//! * [`Graph`](./graph/struct.Graph.html) -
//!   An adjacency list graph with arbitrary associated data.
//! * [`StableGraph`](./stable_graph/struct.StableGraph.html) -
//!   Similar to `Graph`, but it keeps indices stable across removals.
//! * [`GraphMap`](./graphmap/struct.GraphMap.html) -
//!   An adjacency list graph backed by a hash table. The node identifiers are the keys
//!   into the table.
//! * [`MatrixGraph`](./matrix_graph/struct.MatrixGraph.html) -
//!   An adjacency matrix graph.
//! * [`CSR`](./csr/struct.Csr.html) -
//!   A sparse adjacency matrix graph with arbitrary associated data.
//!
//! ### Generic parameters
//!
//! Each graph type is generic over a handful of parameters. All graphs share 3 common
//! parameters, `N`, `E`, and `Ty`. This is a broad overview of what those are. Each
//! type's documentation will have finer detail on these parameters.
//!
//! `N` & `E` are called *weights* in this implementation, and are associated with
//! nodes and edges respectively. They can generally be of arbitrary type, and don't have to
//! be what you might conventionally consider weight-like. For example, using `&str` for `N`
//! will work. Many algorithms that require costs let you provide a cost function that
//! translates your `N` and `E` weights into costs appropriate to the algorithm. Some graph
//! types and choices do impose bounds on `N` or `E`.
//! [`min_spanning_tree`](./algo/fn.min_spanning_tree.html) for example requires edge weights that
//! implement [`PartialOrd`](https://doc.rust-lang.org/stable/core/cmp/trait.PartialOrd.html).
//! [`GraphMap`](./graphmap/struct.GraphMap.html) requires node weights that can serve as hash
//! map keys, since that graph type does not create standalone node indices.
//!
//! `Ty` controls whether edges are [`Directed`](./enum.Directed.html) or
//! [`Undirected`](./enum.Undirected.html).
//!
//! `Ix` appears on graph types that use indices. It is exposed so you can control
//! the size of node and edge indices, and therefore the memory footprint of your graphs.
//! Allowed values are `u8`, `u16`, `u32`, and `usize`, with `u32` being the default.
//!
//! ### Shorthand types
//!
//! Each graph type vends a few shorthand type definitions that name some specific
//! generic choices. For example, [`DiGraph<_, _>`](./graph/type.DiGraph.html) is shorthand
//! for [`Graph<_, _, Directed>`](graph/struct.Graph.html).
//! [`UnMatrix<_, _>`](./matrix_graph/type.UnMatrix.html) is shorthand for
//! [`MatrixGraph<_, _, Undirected>`](./matrix_graph/struct.MatrixGraph.html). Each graph type's
//! module documentation lists the available shorthand types.
//!
//! # Crate features
//!
//! * **serde-1** -
//!   Defaults off. Enables serialization for ``Graph, StableGraph, GraphMap`` using
//!   [`serde 1.0`](https://crates.io/crates/serde). May require a more recent version
//!   of Rust than petgraph alone.
//! * **graphmap** -
//!   Defaults on. Enables [`GraphMap`](./graphmap/struct.GraphMap.html).
//! * **stable_graph** -
//!   Defaults on. Enables [`StableGraph`](./stable_graph/struct.StableGraph.html).
//! * **matrix_graph** -
//!   Defaults on. Enables [`MatrixGraph`](./matrix_graph/struct.MatrixGraph.html).
//!
#![doc(html_root_url = "https://docs.rs/petgraph/0.4/")]

extern crate fixedbitset;
#[cfg(feature = "graphmap")]
extern crate indexmap;

#[cfg(feature = "serde-1")]
extern crate serde;
#[cfg(feature = "serde-1")]
#[macro_use]
extern crate serde_derive;

#[cfg(all(feature = "serde-1", test))]
extern crate itertools;

#[doc(no_inline)]
pub use crate::graph::Graph;

pub use crate::Direction::{Incoming, Outgoing};

#[macro_use]
mod macros;
mod scored;

// these modules define trait-implementing macros
#[macro_use]
pub mod visit;
#[macro_use]
pub mod data;

pub mod adj;
pub mod algo;
pub mod csr;
pub mod dot;
#[cfg(feature = "generate")]
pub mod generate;
mod graph_impl;
#[cfg(feature = "graphmap")]
pub mod graphmap;
mod iter_format;
mod iter_utils;
#[cfg(feature = "matrix_graph")]
pub mod matrix_graph;
#[cfg(feature = "quickcheck")]
mod quickcheck;
#[cfg(feature = "serde-1")]
mod serde_utils;
mod traits_graph;
pub mod unionfind;
mod util;

pub mod operator;
pub mod prelude;

/// `Graph<N, E, Ty, Ix>` is a graph datastructure using an adjacency list representation.
pub mod graph {
    pub use crate::graph_impl::{
        edge_index, node_index, DefaultIx, DiGraph, Edge, EdgeIndex, EdgeIndices, EdgeReference,
        EdgeReferences, EdgeWeightsMut, Edges, EdgesConnecting, Externals, Frozen, Graph,
        GraphIndex, IndexType, Neighbors, Node, NodeIndex, NodeIndices, NodeReferences,
        NodeWeightsMut, UnGraph, WalkNeighbors,
    };
}

#[cfg(feature = "stable_graph")]
pub use crate::graph_impl::stable_graph;

// Index into the NodeIndex and EdgeIndex arrays
/// Edge direction.
#[derive(Clone, Copy, Debug, PartialEq, PartialOrd, Ord, Eq, Hash)]
#[repr(usize)]
pub enum Direction {
    /// An `Outgoing` edge is an outward edge *from* the current node.
    Outgoing = 0,
    /// An `Incoming` edge is an inbound edge *to* the current node.
    Incoming = 1,
}

impl Direction {
    /// Return the opposite `Direction`.
    #[inline]
    pub fn opposite(self) -> Direction {
        match self {
            Outgoing => Incoming,
            Incoming => Outgoing,
        }
    }

    /// Return `0` for `Outgoing` and `1` for `Incoming`.
    #[inline]
    pub fn index(self) -> usize {
        (self as usize) & 0x1
    }
}

#[doc(hidden)]
pub use crate::Direction as EdgeDirection;

/// Marker type for a directed graph.
#[derive(Clone, Copy, Debug)]
pub enum Directed {}

/// Marker type for an undirected graph.
#[derive(Clone, Copy, Debug)]
pub enum Undirected {}

/// A graph's edge type determines whether it has directed edges or not.
pub trait EdgeType {
    fn is_directed() -> bool;
}

impl EdgeType for Directed {
    #[inline]
    fn is_directed() -> bool {
        true
    }
}

impl EdgeType for Undirected {
    #[inline]
    fn is_directed() -> bool {
        false
    }
}

/// Convert an element like `(i, j)` or `(i, j, w)` into
/// a triple of source, target, edge weight.
///
/// For `Graph::from_edges` and `GraphMap::from_edges`.
pub trait IntoWeightedEdge<E> {
    type NodeId;
    fn into_weighted_edge(self) -> (Self::NodeId, Self::NodeId, E);
}

impl<Ix, E> IntoWeightedEdge<E> for (Ix, Ix)
where
    E: Default,
{
    type NodeId = Ix;

    fn into_weighted_edge(self) -> (Ix, Ix, E) {
        let (s, t) = self;
        (s, t, E::default())
    }
}

impl<Ix, E> IntoWeightedEdge<E> for (Ix, Ix, E) {
    type NodeId = Ix;
    fn into_weighted_edge(self) -> (Ix, Ix, E) {
        self
    }
}

impl<'a, Ix, E> IntoWeightedEdge<E> for (Ix, Ix, &'a E)
where
    E: Clone,
{
    type NodeId = Ix;
    fn into_weighted_edge(self) -> (Ix, Ix, E) {
        let (a, b, c) = self;
        (a, b, c.clone())
    }
}

impl<'a, Ix, E> IntoWeightedEdge<E> for &'a (Ix, Ix)
where
    Ix: Copy,
    E: Default,
{
    type NodeId = Ix;
    fn into_weighted_edge(self) -> (Ix, Ix, E) {
        let (s, t) = *self;
        (s, t, E::default())
    }
}

impl<'a, Ix, E> IntoWeightedEdge<E> for &'a (Ix, Ix, E)
where
    Ix: Copy,
    E: Clone,
{
    type NodeId = Ix;
    fn into_weighted_edge(self) -> (Ix, Ix, E) {
        self.clone()
    }
}