As far as I know, the property of a Markov Random Field is defined as follows:

Let $G = (V, E)$ be a Markov Network. Let $X, Y, C \subseteq V$. If every path from a vertex in $X$ to a vertex in $Y$ passes through a vertex in $C$, then we may say that $X$ and $Y$ are conditionally independent given $C$.

However, I have some conflicting information about whether this statement should be a biconditional (depending on the source I reference). Namely, I'm wondering if the following is true:

If there exists a path from $X$ to $Y$ which does not pass through a vertex in $C$, can we say that $X$ and $Y$ are necessarily not independent given $C$.


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