## Expand description

`petgraph`

is a graph data structure library.

Graphs are collections of nodes, and edges between nodes. `petgraph`

provides several graph types (each differing in the
tradeoffs taken in their internal representation),
algorithms on those graphs, and functionality to
output graphs in
`graphviz`

format. Both nodes and edges
can have arbitrary associated data, and edges may be either directed or undirected.

## Example

```
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`

- An adjacency list graph with arbitrary associated data.`StableGraph`

- Similar to`Graph`

, but it keeps indices stable across removals.`GraphMap`

- An adjacency list graph backed by a hash table. The node identifiers are the keys into the table.`MatrixGraph`

- An adjacency matrix graph.`CSR`

- 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`

for example requires edge weights that
implement `PartialOrd`

.
`GraphMap`

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`

or
`Undirected`

.

`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<_, _>`

is shorthand
for `Graph<_, _, Directed>`

.
`UnMatrix<_, _>`

is shorthand for
`MatrixGraph<_, _, Undirected>`

. Each graph type’s
module documentation lists the available shorthand types.

## Crate features

**serde-1**- Defaults off. Enables serialization for`Graph, StableGraph`

using`serde 1.0`

. May require a more recent version of Rust than petgraph alone.**graphmap**- Defaults on. Enables`GraphMap`

.**stable_graph**- Defaults on. Enables`StableGraph`

.**matrix_graph**- Defaults on. Enables`MatrixGraph`

.

## Re-exports

## Modules

- Simple adjacency list.
- Graph algorithms.
- Compressed Sparse Row (CSR) is a sparse adjacency matrix graph.
- Graph traits for associated data and graph construction.
- Simple graphviz dot file format output.
`Graph<N, E, Ty, Ix>`

is a graph datastructure using an adjacency list representation.`GraphMap<N, E, Ty>`

is a graph datastructure where node values are mapping keys.`MatrixGraph<N, E, Ty, NullN, NullE, Ix>`

is a graph datastructure backed by an adjacency matrix.- Commonly used items.
`StableGraph`

keeps indices stable across removals.`UnionFind<K>`

is a disjoint-set data structure.- Graph traits and graph traversals.

## Enums

- Marker type for a directed graph.
- Edge direction.
- Marker type for an undirected graph.

## Traits

- A graph’s edge type determines whether it has directed edges or not.
- Convert an element like
`(i, j)`

or`(i, j, w)`

into a triple of source, target, edge weight.