I am reading CPDAG, can anyone please explain why G1 and G3 are not equivalence classes as in the picture below? Thank you very much!
according to https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume18/acid03a-html/node2.html .
"Theorem 1 [59] Two DAGs are equivalent if and only if they have the same skeleton and the same v-structures.
The skeleton of a DAG is the undirected graph that results from ignoring the directionality of every edge.
A v-structure in a DAG $H$ is an ordered triplet of nodes, $(x,y,z)$, such that (1) $H$ contains the arcs $x\rightarrow y$ and $y \leftarrow z$, and (2) the nodes $x$ and $z$ are not adjacent in $H$. A head-to-head pattern (shortened h-h) in a DAG $H$ is an ordered triplet of nodes, $(x,y,z)$, such that $H$ contains the arcs $x\rightarrow y$ and $y \leftarrow z$. Note that in an h-h pattern $(x,y,z)$ the nodes $x$ and $z$ can be adjacent."
The concept of equivalence of DAGs partitions the space of DAGs into a set of equivalence classes.