A new model of communication network topologies for multiprocessor systems and networks-on-chip is proposed. A class of parametrically defined regular multi-level networks (graphs) is introduced, which allow using as level elements most of the known regular graphs proposed earlier as structures of computing systems, combining them in an optimal way. To construct multi-level networks, an operation of multi-level composition is introduced, which consists of two steps: (1) a disjoint union of graphs of all levels and (2) the sum of two graphs – the graph obtained in the first step and the graph connecting all levels. In this paper, we apply the operation of multi-level composition to circulant graphs. To synthesize a new class of topologies, an algorithm for simulated annealing is used to determine the optimal parameters of the communication network topology that minimize the average network distance for a given number of nodes, number of levels, and node degree. The program for synthesizing optimal networks is developed using large language models (LLM) and implemented in sequential and parallel versions on the Kunpeng processor. The introduced multi-level networks made it possible to obtain better structural characteristics than circulant networks with the same equipment costs.