Can such a search pattern (based on the neighbourhood) be designed?

[lichengzhang1]

I want to filter graphs that satisfy that $|N(x)\cup N(y)|\ge \frac{2(n-1)}{3}$ for any $xy\notin E(G)$?

Note that $N(v)$ refers to the neighborhood of a vertex $v$.

First, I did not see the "N(x) function" in the GraphFilter software, and I did not see the union of sets, let alone any options for arbitrary non-adjacent vertices.

This is just an example. Some of the chemical indices in chemical graph theory are also built on top of the neighbourhood of the vertices. The software could be more free.