Concentrators and generalized-concentrators are interconnection networks that provide respectively pairwise vertex-disjoint directed paths and trees to satisfy interconnection requests. An interconnection network is non-blocking in the strict sense if every compatible interconnection request can be satisfied by a path regardless of any existing interconnections. We present an interconnection property equivalent to the generalized-concentration with constrained network capacity and request multiplicity in the strictly non-blocking context, and show a polynomial-time computational complexity result for deciding the strictly non-blocking generalized-concentration properties with constrained network parameters, by using b-matching techniques.