#graph #strongly-connected #scc #toposort #tarjan


Find the strongly-connected components of a graph with nodes labeled by integer ids

2 releases

0.1.1 May 21, 2022
0.1.0 May 21, 2022

#1471 in Algorithms

MIT license

277 lines


Download: crates.io/crates/id_graph_sccs

Docs: docs.rs/id_graph_sccs

A small crate for finding the strongly-connected components of a directed graph.

This crate is built on the id_collections crate, and is designed to work with graphs in which nodes are labeled by integer indices belonging to a contiguous range from zero to some upper bound. The edges of the input graph do not need to be stored in any particular format; the caller provides the outgoing edges for each node via a callback function which is invoked lazily as the algorithm traverses the graph.

The implementation of the algorithm does not rely on recursion, so it is safe to run it on arbitrarily large graphs without risking a stack overflow.


use id_collections::{id_type, IdVec};
use id_graph_sccs::{find_components, Sccs, Scc, SccKind};

struct NodeId(u32);

struct SccId(u32);

// Note: you are not required to store the edges of the input graph in an 'IdVec'; all that
// matters is that you are able to pass a closure to the 'find_components' function which
// returns the edges for a given node.
let mut graph: IdVec<NodeId, Vec<NodeId>> = IdVec::new();

let node_a = graph.push(Vec::new());
let node_b = graph.push(Vec::new());
let node_c = graph.push(Vec::new());
let node_d = graph.push(Vec::new());

graph[node_a].extend([node_a, node_b]);
graph[node_c].extend([node_b, node_d]);

let sccs: Sccs<SccId, NodeId> = find_components(graph.count(), |node| &graph[node]);

// We can iterate over 'sccs' to obtain the components of the graph:
let mut components: Vec<Scc<NodeId>> = Vec::new();
for (_scc_id, component) in &sccs {

assert_eq!(components.len(), 3);

assert_eq!(components[0].kind, SccKind::Acyclic);
assert_eq!(components[0].nodes, &[node_d]);

assert_eq!(components[1].kind, SccKind::Cyclic);

assert_eq!(components[2].kind, SccKind::Cyclic);
assert_eq!(components[2].nodes, &[node_a]);


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