The Markov condition (sometimes called Markov assumption) for a Bayesian network states that any node in a Bayesian network is conditionally independent of its nondescendents, given its parents.
A node is conditionally independent of the entire network, given its Markov blanket.
The related causal Markov condition is that a phenomenon is independent of its noneffects, given its direct causes. In the event that the structure of a Bayesian network accurately depicts causality, the two conditions are equivalent. However, a network may accurately embody the Markov condition without depicting causality, in which case it should not be assumed to embody the causal Markov condition.
References
Causal Markov condition Wikipedia(Text) CC BY-SA