[Math] Does this linear algebra construction based on a graph have a name, and where has it been studied

Question

In the paper Kochen-Specker set with seven contexts by Lisonek, Badziag, Portillo and Cabello, the following construction is used :

Question : Have such constructions been used elsewhere, and if so what are recommended papers and books on that topic ?

Thank you.

Answer 1

This looks like a close relative of the Hamming graph: Vertices of the Hamming graph in question are $2-$element subsets of $\{1,\dots,7\}$. Edges join vertices corresponding to subsets intersecting in an element. Your graph is the Hamming graph with "overlaid edges" (two vertices are adjacent if they are on a straight segment).