Question about Complete partially Directed Acyclic Graph 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 .

&quot;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.&quot;
The concept of equivalence of DAGs partitions the space of DAGs into a set of equivalence classes.
They have different v-structures: $G_1$ has the v-structures $(x_3,y,x_4),(x_4,y,x_3)$, whereas $G_3$ has the v-structures $(x_1,x_4,y),(y,x_4,x_1)$.