Let $G_1=(V,E_1)$ and $G_2=(V,E_2)$ be directed acyclic graphs on the same finite vertex set $V$, where $E_i\subset V\times V$ and no edge has the form $(v,v)$. For a directed acyclic graph $G=(V,E)$, write $x\sim_G y$ when either $(x,y)\in E$ or $(y,x)\in E$; the skeleton of $G$ is the undirected graph on $V$ with edge set $\{\{x,y\}:x\neq y\text{ and }x\sim_G y\}$. A vertex $u$ is a parent of $v$ in $G$ if $(u,v)\in E$, and a vertex $w$ is a descendant of $v$ if there is a directed path in $G$ from $v$ to $w$, with the path of length zero allowed. An unshielded collider, equivalently a v-structure, is an ordered triple $(a,b,c)$ of distinct vertices such that $a\sim_G b$, $b\sim_G c$, $a\not\sim_G c$, and $(a,b),(c,b)\in E$.

A path $(v_0,\dots,v_m)$ in the skeleton of $G$ is d-connecting given $C\subset V$ if every internal noncollider on the path is outside $C$ and every internal collider on the path has a descendant in $C$. Two subsets $A,B\subset V$ are d-separated by $C\subset V$ if there is no d-connecting path given $C$ from a vertex of $A$ to a vertex of $B$. For $i\in\{1,2\}$, let $\mathcal I(G_i)$ be the d-separation model of $G_i$, namely the collection of all triples $(A,B,C)$ of pairwise disjoint subsets of $V$ such that $A$ and $B$ are d-separated by $C$ in $G_i$.

Then the following are equivalent:

1. $G_1$ and $G_2$ are Markov equivalent, that is,

\begin{align*} \mathcal I(G_1)=\mathcal I(G_2). \end{align*}

2. $G_1$ and $G_2$ have the same skeleton and the same unshielded colliders.

Equivalently, $G_1$ and $G_2$ are Markov equivalent if and only if they have the same skeleton and the same v-structures.