Remove petgraph from bevy_ecs (#15519)

# Objective

- Contributes to #15460

## Solution

- Removed `petgraph` as a dependency from the `bevy_ecs` crate.
- Replaced `TarjanScc` and `GraphMap` with specialised in-tree
alternatives.

## Testing

- Ran CI locally.
- Added new unit tests to check ordering invariants.
- Confirmed `petgraph` is no longer present in `cargo tree -p bevy_ecs`

## Migration Guide

The `Dag::graph` method no longer returns a `petgraph` `DiGraph` and
instead returns the new `DiGraph` type within `bevy_ecs`. Edge and node
iteration methods are provided so conversion to the `petgraph` type
should be trivial if required.

## Notes

- `indexmap` was already in the dependency graph for `bevy_ecs`, so its
inclusion here makes no difference to compilation time for Bevy.
- The implementation for `Graph` is heavily inspired from the `petgraph`
original, with specialisations added to simplify and improve the type.
- `petgraph` does have public plans for `no_std` support, however there
is no timeframe on if or when that functionality will be available.
Moving to an in-house solution in the interim allows Bevy to continue
developing its `no_std` offerings and further explore alternate graphing
options.

---------

Co-authored-by: Lixou <[email protected]>
Co-authored-by: vero <[email protected]>

Author: 3 people

crates/bevy_ecs/Cargo.toml

@@ -27,7 +27,6 @@ bevy_tasks = { path = "../bevy_tasks", version = "0.15.0-dev" }
 bevy_utils = { path = "../bevy_utils", version = "0.15.0-dev" }
 bevy_ecs_macros = { path = "macros", version = "0.15.0-dev" }
 
-petgraph = "0.6"
 bitflags = "2.3"
 concurrent-queue = "2.5.0"
 disqualified = "1.0"
@@ -43,6 +42,7 @@ derive_more = { version = "1", default-features = false, features = [
 nonmax = "0.5"
 arrayvec = { version = "0.7.4", optional = true }
 smallvec = { version = "1", features = ["union"] }
+indexmap = { version = "2.5.0", default-features = false, features = ["std"] }
 variadics_please = "1.0"
 
 [dev-dependencies]

crates/bevy_ecs/src/schedule/config.rs

@@ -3,7 +3,7 @@ use variadics_please::all_tuples;
 use crate::{
     schedule::{
         condition::{BoxedCondition, Condition},
-        graph_utils::{Ambiguity, Dependency, DependencyKind, GraphInfo},
+        graph::{Ambiguity, Dependency, DependencyKind, GraphInfo},
         set::{InternedSystemSet, IntoSystemSet, SystemSet},
         Chain,
     },