1. A switching system comprising: a plurality of input switching modules, each of said input switching modules having several input-switching-module inputs which are network inputs, several input-switching-module outputs, and input-switching-module switching control means for connecting each of said input-switching-module inputs to any one of said input-switching module outputs in response to control signals; a plurality of output switching modules, each of said output switching modules having several output-switching-module inputs, several output-switching-module outputs which are network outputs, and output-switching-module switching control means for connecting each of said output-switching-module inputs to any one of said output-switching module outputs in response to control signals; a plurality of center switching modules, each of said center switching modules having several center-switching-module inputs, several center-switching-module outputs, and center-switching-module switching control means for connecting each of said center-switching-module inputs to any one of said center-switching-module outputs in response to control signals; a first plurality of links, each link of said first plurality connecting a different one of said input-switching-module outputs to a different one of said center-switching-module inputs; a second plurality of links, each link of said second plurality connecting a different one of said center-switching-module outputs to a different one of said output-switching-module inputs; a switch memory means having a plurality of memory cells, each of said memory cells having an address related to a link in one of said pluralities of links, each of said memory cells storing a first information unit indicating which of the network inputs should be connected to the link associated with the cell address and also storing a second information unit indicating which of the network outputs should be connected to the link associated with the cell address; control signal generating means responsive to the information units stored in said memory cell for generating control signals fed to the switching control means on said switching modules to effect the connections between network inputs and network outputs as recorded in said memory cells; means for receiving information units representing a first network input and a first network output between which a connection is desired; means for locating a first memory cell storing the information unit of said first network input and for locating a second memory cell storing the information unit of the first network output; means for interchanging information units recorded in said first and second memory cells so that the information units of said first network input and said first network output go into the same memory cell; and analyzing means for determining whether the new connections established by said switching modules in response to the new information units recorded in said first and second memory cells correspond to the desired connection.