Belief networks: independence

It's not immediately obvious how to interpret the conditional relationships represented by a belief network. For example, consider the networks below.

Network(s) [...] represent the distribution:

Network(s) [...] represent the distribution:

Next, consider conditional independence.

• In a), $x$ and $y$ are unconditionally dependent, and conditioned on $z$ they are independent. Knowing either gives information on the distribution of $z$, which in turn informs of the others distribution.. $p(x,y|z)=p(x|z)p(y|z)$
• In b), $x$ and $y$ are unconditionally dependent, and conditioned on $z$ they are independent. $p(x,y|z)\propto p(z|x)p(x)p(y|z)$
• In c), $x$ and $y$ are unconditionally independent, and conditioned on $z$ they are dependent. $p(x,y|z)\propto p(z|x,y)p(x)p(y)$
• Id d), $x$ and $y$ are unconditionally independent, and conditioned on $z$ or $w$, are dependent. See book for full equation.