antichains¶

antichains(G, topo_order=None)[source]¶

Generates antichains from a directed acyclic graph (DAG).

An antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable.

Parameters

GNetworkX DiGraph: A directed acyclic graph (DAG)
topo_order: list or tuple, optional: A topological order for G (if None, the function will compute one)

Yields

antichainlist: a list of nodes in G representing an antichain

Raises

NetworkXNotImplemented: If G is not directed
NetworkXUnfeasible: If G contains a cycle

Notes

This function was originally developed by Peter Jipsen and Franco Saliola for the SAGE project. It’s included in NetworkX with permission from the authors. Original SAGE code at:

https://github.com/sagemath/sage/blob/master/src/sage/combinat/posets/hasse_diagram.py

References

1: Free Lattices, by R. Freese, J. Jezek and J. B. Nation, AMS, Vol 42, 1995, p. 226.

Examples

>>> DG = nx.DiGraph([(1, 2), (1, 3)])
>>> list(nx.antichains(DG))
[[], [3], [2], [2, 3], [1]]