There's a useful concept for analyzing BNs, which is directed separation (d-separation). We say that sets (or variables) X, Y are d-separated if all the paths between them are blocked. For example, if we have a graph containing Z->X and Z->Y, X and Y are not d-separated because there's an unblocked path between X and Y. But, if we condition on Z, then X and Y are d-separated. Another way of putting this is that once we know Z's value, X and Y are independent. Note that we are associating dependence with connectedness.

In other words, d-separation is especially useful for understanding which sets of variables are independent/dependent of other ones. This is particularly useful when we have large networks with hundreds of arcs (in these cases, visual inspection cannot be done):

dsep(dag,"travel_time","Recently_had_child")
dsep(dag,"travel_time","Sleep_quality")
dsep(dag,"travel_time","Sleep_quality","Area")

After running the preceding, we'll get the following output: