@adam2392 What does this sign mean?

V •→X

Does it mean that the mark at the V end can be anything or that this can be a path of arbitrary length with the last mark being an arrow pointing towards X?

That is answered on pg2 of https://auai.org/uai2015/proceedings/papers/155.pdf.

Lmk if you have other questions too.

Does a function already exists to find if a collider path exists between two nodes in a graph?

Does a function already exists to find if a collider path exists between two nodes in a graph?

I don't think so, but all_vstructures is similar, so you can modify that implementation to get a new function all_collider_paths(src, target, G).

@adam2392 The paper says:

A path of length one is a trivial collider path.

Do they mean a triple? (Only counting the non-endpoint node for the length) Because I don't see how a path could be a collider path otherwise.

@adam2392 The paper says:

A path of length one is a trivial collider path.

Do they mean a triple? (Only counting the non-endpoint node for the length) Because I don't see how a path could be a collider path otherwise.

I think they just mean a path of length one. So a single variable path is a collider, but yeah you would really only look at the path between two points usually.

So a collider path is a sequence of variables <X_1, X_2, X_3, …, X_i>, where you just look at the edges between each consecutive triple <X_i-1, X_i, X_i+1> in that path to determine if they meet the collider condition.