As J.D.Dixon noted in his great book; Permutations Group, we can speak about Strong Primitivity of a group acting on a set $\Omega$ by means of orbital graphs. The way he paved employes digraphs prove if such a group is strong primitive or not. I referred to another reference came from P.J.Cameron (Toplogy in permutation groups) to find additional information. He cited that Wielandt observed that primitivity is not strong enough. Cameron continues by illustrating an example:
Let $G$ is a primitive group on a finite set $\Omega$ and let $\Delta$ be a non-empty proper subset of $\Omega$. then the following seperation property holds: for any distinct $\alpha$, $\beta$ $\in$ $\Omega$, there exists $g\in G$ with $\alpha^g$ $\in \Delta$ and $\beta^g$ $\notin \Delta$. This fails for infinite primitive groups.
and that is why Wielandt proposed the property of Strong Primitivity. Honestly, I didn't get much of what Cameron noted and need someone to elaborate. Why such a condition's named separate property? Thanks.