This paper is devoted to non-blocking optoelectronic networks in which group operations over a set of numbers are executed during the transmission of one number. The execution of group operations by photonic units placed at each network user is considered, and the circuitry of these units is presented. The possibility of executing group operations in cyclic sequences of nodes defined by Hamilton graphs is investigated. Procedures for constructing such cyclic sequences and executing group operations in them are proposed. The possibility of designing a non-blocking electronic system area network for any number of users is studied. A method for designing an optoelectronic network as a tandem network with optoelectronic switches controlled by their analogs from the electronic network is described.