What we have seen above is that:
1. In a serial connection from B to C via A, evidence from B to C is blocked only when we have hard evidence about A.
2. In a diverging connection where B and C have the common parent A evidence from B to C is blocked only when we have hard evidence about A.
3. In a converging connection where A has parents B and C any evidence about A results in evidence transmitted between B and C.
In cases 1 and 2 we say that the nodes B and C are d-separated when there is hard evidence of A. In case 3 B and C are only d-separated when there is no evidence about A In general two nodes which are not d-separated are said to be d-connected.
These three cases enable us to determine in general whether any two nodes in a given BBN are dependent (d-connected) given the evidence entered in the BBN. Formally:
Definition of d-separation: Two nodes X and Y in a BBN are d-separated if, for all paths between X and Y, there is an intermediate node A for which either:
1. the connection is serial or diverging and the state of A is known for certain; or
2. the connection is converging and neither A (nor any of its descendants) have received any evidence at all.