GSN is a generalization of shuffle-exchange networks and it can represent a family of network structures (including ShuffleNet & de Bruijn graph) for an arbitrary number of nodes. GSN employs a regular interconnection graph with highly desirable properties and it can serve as a logical (virtual), multihop topology for constructing the next generation of lightwave networks using wavelength-division multiplexing (WDM). GSN can be divided into two classes: extra-stage and reduced-stage. The architecture of the GSN is introduced briefly. Then, the performance of the GSN is analyzed. At last an algorithm for computing the average hop distance for the reduced-stage GSN is proposed in this paper.