# Why this could not be represented by a Bayesian network

A, B, C, D are four variables. Why $$A \perp C | \{ B , D \}$$ and $$B \perp D | \{ A , C \}$$ could not be represented by a Bayesian network?

• This is an example discussed in the book "Probabilistic Graphical Models" by Koller and Friedman. The reason why these conditional independence assumptions cannot simultaneously be encoded in a Bayesian network can be proven by simply drawing all possible Bayesian Networks over four random variables, and concluding that none of them encodes both assumptions correctly. – Maurits M Jul 24 at 13:56