strongly_connected_components#

strongly_connected_components(G)[source]#

Generate nodes in strongly connected components of graph.

Parameters:

GNetworkX Graph: A directed graph.

Returns:

compgenerator of sets: A generator of sets of nodes, one for each strongly connected component of G.

Raises:

NetworkXNotImplemented: If G is undirected.

See also

connected_components
weakly_connected_components
kosaraju_strongly_connected_components

Notes

Iterative version of Tarjan’s algorithm using the improvements described by Tarjan and Zwick in their survey [1], plus a trick borrowed from the Rust implementation of the WebGraph framework [2].

References

[1]

Robert E. Tarjan and Uri Zwick, “Finding strong components using depth-first search”, European Journal of Combinatorics, 119, 2024. https://doi.org/10.1016/j.ejc.2023.103815

[2]

Tommaso Fontana, Sebastiano Vigna, and Stefano Zacchiroli, “WebGraph: The next generation (is in Rust)”, Companion Proceedings of the ACM Web Conference 2024, pp. 686-689, 2024. https://doi.org/10.1145/3589335.3651581

Examples

Generate a sorted list of strongly connected components, largest first.

>>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
>>> nx.add_cycle(G, [10, 11, 12])
>>> [
...     len(c)
...     for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True)
... ]
[4, 3]

If you only want the largest component, it’s more efficient to use max instead of sort.

>>> largest = max(nx.strongly_connected_components(G), key=len)