Inferring Social Ties
This model seems a little confusing due to the role of $G$ and I didn't find their definition of $P(Y|G)$ very sound.

You can consider it the following way:

$$P(Y|\textbf{X},G) \propto P(\textbf{X}|Y) \cdot P(G|Y) \cdot P(Y) = P(\textbf{X}|Y) \cdot [P(G|Y) \cdot P(Y)] \propto P(\textbf{X}|Y) \cdot P(Y|G)$$