The main approaches to the synthesis of networks-on-chip based on regular and specialized topologies are analyzed. The optimality criteria of the topologies of networks-on-chip and a new class of quasi-optimal topologies and methods for their synthesis are proposes. The requirements for quasi-optimal topologies are defined. By using the mathematical methods of optimization the analysis of the obtained quasi-optimal topologies for the number of nodes of 25 is performed. It is shown, that their properties are close to the theoretically possible optimal topologies to not less than 96.3%.