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.

[atilaajones]

Hello
First we would like to thank you for contacting us, it is very important this feedback from the community.

The GraphFilter does not actually have the vertex neighborhood function, in fact the filtering only has functions that are inherent to the graph. The implementation of functions that use two (or more) graphs or that observe vertices are part of the future project. So it's really not possible to insert, for now, a logical condition with the specificity you requested.

We are currently working on releasing a new version, we will discuss the feasibility of implementing this type of filtering function.
Again thank you for contacting us.