How would we measure the non-randomness and compactness of this cubic lattice and corresponding graph?

Question

The genetic code is decrypted into a 4x4x4 cubic lattice shown here:

https://www.researchgate.net/publication/361073909_Decryption_and_Topology_of_the_Genetic_Code

That cube was used to construct an un-direction graph with 21 nodes and 148 edges in Mathematica - displayed below:

Answer 1

Designated Cube 1, the order: g, a, c, u yields a structure with the most closed-loops. The mirror of this cube (u, c, a, g) is a second solution.

(21) (PDF) Graph Analysis of the Genetic Code Using Closed-Loops Shows Isotropic Axes Using the Order GACU Yields Maximum Topological Compactness. Available from: https://www.researchgate.net/publication/361250677_Graph_Analysis_of_the_Genetic_Code_Using_Closed-Loops_Shows_Isotropic_Axes_Using_the_Order_GACU_Yields_Maximum_Topological_Compactness [accessed Jun 14 2022]. Computational proof, but someone should try group theory: