A circuit switching system in an M-ary, n-cube connected network completes a best-first path from an originating node to a destination node by latching valid legs of the path as the path is being sought out. Each network node is provided with a routing hyperswitch sub-network, ("HSN") connected between that node and bidirectional high capacity communication channels of the n-cube network. The sub-networks are all controlled by routing algorithms which respond to message identification headings ("headers") on messages to be routed along one or more routing legs. The header includes information embedded therein which is interpreted by each sub-network to route and historically update the header. A logic circuit, available at every node, implements the algorithm and automatically forwards or back-tracks the header in the network legs of various paths until a completed path is latched.