Three random variables $X$, $Y$ and $Z$ have a joint (trivariate) distribution. How to tell/calculate if there are dyadic relationships between the variables, or triadic relationships between them?
I guess dyadic means pair-wise or two-way co-dependency, whereas triadic means three-way relationship, but not sure
Consider the following DAG: $Y \rightarrow X \leftarrow Z$. The dependence implied by this would be $Y\not\!\perp\!\!\!\perp Z | X$, which can be checked given $P(X,Y,Z)$. Similarly for $X \rightarrow Y \leftarrow Z$ and $X \rightarrow Z \leftarrow Y$. The cases where one or more arrows are deleted from the above ones should also be straightforward to check. Is this what you were looking for?