How to determine if two directed probabilistic graphical models are I-equivalent? I'm trying to figure out how to determine if these two models are I-equivalent. Google didn't properly give me a solid answer so far. Any idea on to determine it?
Thank you.

 A: Equivalence definition matters here. But, I-equivalence is a common query in Bayesian Networks, in which I just assumed you're asking for that, but you need to specify in your question as well. For two BNs to be I-equivalent, they need to have the same skeleton, and immoralities. Check the lecture here. Immorality is defined as a V-structure that a node $X$, having parents $Y,Z$ without an edge in between them. 
In your graphs, the skeletons are clearly the same. And, the only V-structure in both graphs is the $B,C,D$ triple. So, the two graphs have the same V-structures and they are I-equivalent.
A: You can read section 9 of this article and this piece of information would be helpful: 

I-equivalence can be determined by looking at the skeleton graphs,
  i.e. the graphs formed by converting directed edges to undirected
  edges. Two graphs are I-equivalent if they have the same skeleton and
  the same set of v-structures

In your case, you just compare the v-structures in each graph(both contain only $B\rightarrow C \leftarrow D$) and remove the direction to compare the skeleton(the same), so they are I-equivalent. 
