 (ii) The Faithfulness Condition. The Faithfulness Condition (FC) is the converse of the Markov Condition: it says that all of the (conditional and unconditional) probabilistic independencies that exist among the variables in \(\bV\) are required by the MC. For example, suppose that \(\bV = \{X, Y, Z\}\). Suppose also that X and Z are unconditionally independent of one another, but dependent, conditional upon Y. (The other two variable pairs are dependent, both conditionally and unconditionally.) The graph shown in  Figure 8  does not satisfy FC with respect to this distribution (colloquially, the graph is not faithful to the distribution). MC, when applied to the graph of Figure 8, does not imply the independence of X and Z. This can be seen by noting that X and Z are d-connected (by the empty set): neither the path \(X \rightarrow Z\) nor \(X \rightarrow Y\rightarrow Z\) is blocked (by the empty set). By contrast, the graph shown in  Figure 7  above is faithful to the described distribution. Note that Figure 8 does satisfy the Minimality Condition with respect to the distribution; no subgraph satisfies MC with respect to the described distribution. In fact, FC is strictly stronger than the Minimality Condition.