Discovery of infinite families of optimal double-loop networks with a given template of generators

Optimal ring circulant networks of degree four are considered as models of reliable communication networks with minimal delays for networks on a chip and multiprocessor cluster systems. Based on the analysis of a data set of optimal descriptions of double-loop networks, a search has been carried out for analytically determined infinite families of optimal graphs. By integrating data visualization and analytical descriptions of optimal graphs, new infinite families of optimal networks with a linear generator of the form $s=4d+\alpha$, where $d$ is the diameter of the graph, have been constructed and theoretically justified. The proposed approach to obtaining families of optimal networks is new and is of interest for further studies of the properties of optimal double-loop networks.