v_structures#

v_structures(G)[source]#

Yields 3-node tuples that represent the v-structures in G.

Colliders are triples in the directed acyclic graph (DAG) where two parent nodes point to the same child node. V-structures are colliders where the two parent nodes are not adjacent. In a causal graph setting, the parents do not directly depend on each other, but conditioning on the child node provides an association.

Parameters:

Ggraph: A networkx DiGraph.

Yields:

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

Raises:

NetworkXNotImplemented: If G is an undirected graph.

See also

colliders

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]

Pearl’s PRIMER Ch-2 page 50: v-structures def.

[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.v_structures(G))
[(0, 4, 2), (0, 5, 1), (4, 5, 1)]