colliders#

Yields 3-node tuples that represent the colliders in G.

In a Directed Acyclic Graph (DAG), if you have three nodes A, B, and C, and there are edges from A to C and from B to C, then C is a collider [1] . In a causal graph setting, this means that both events A and B are “causing” C, and conditioning on C provide an association between A and B even if no direct causal relationship exists between A and B.

Parameters:

Ggraph: A networkx DiGraph.

Yields:

A 3-tuple representation of a collider: Each collider is a 3-tuple with the parent, collider, and other parent.

Raises:

NetworkXNotImplemented: If G is an undirected graph.

See also

v_structures

Notes

This function was written to be used on DAGs, however it works on cyclic graphs too. Since colliders are referred to in the cyclic causal graph literature [2] we allow cyclic graphs in this function. It is suggested that you test if your input graph is acyclic as in the example if you want that property.

References

[1]

Wikipedia: Collider in causal graphs

[2]

A Hyttinen, P.O. Hoyer, F. Eberhardt, M J ̈arvisalo, (2013) “Discovering cyclic causal models with latent variables: a general SAT-based procedure”, UAI’13: Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, pg 301–310, doi:10.5555/3023638.3023669

Examples

>>> G = nx.DiGraph([(1, 2), (0, 4), (3, 1), (2, 4), (0, 5), (4, 5), (1, 5)])
>>> nx.is_directed_acyclic_graph(G)
True
>>> list(nx.dag.colliders(G))
[(0, 4, 2), (0, 5, 4), (0, 5, 1), (4, 5, 1)]