Now I understand this network, then they go on with explaining Pearl's Network Construction algorithm. They have given examples on how the network will change if the ordering of the nodes presented to the algorithm is different. Let's take the node names to be their first letters in capitals $<P, S, C, X, D>$ . Now suppose we present the following order to this algorithm $<D, X, C, P, S>$ . So the network becomes now
I am not able to understand the addition of the final node. When we add $S$ to the network it says
When the final node, Smoker, is added, not only is an arc required from C to S, but another from P to S. In our story S and P are independent, but in the new network, without this final arc, P and S are made dependent by having a common cause, so that effect must be counterbalanced by an additional arc.
Can anyone help me out here. How does this get counterbalanced, maybe some form of equations to show that. Thanks !