As important as the local Markov assumption is, it only gives us information about the independencies in 𝑃 that a DAG implies. It does not even tell us that if 𝑋 and 𝑌 are adjacent in the DAG, then 𝑋 and 𝑌 are dependent. And this additional information is very commonly assumed in causal DAGs. To get this guaranteed dependence between adjacent nodes, we will generally assume a slightly stronger assumption than the local Markov assumption: minimality