A three-stage network is operated in strictly nonblocking manner includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m≧└√{square root over (r2)}┘*MIN(n1,n2) when └√{square root over (r2)}┘ is >1 and odd, or when └√{square root over (r2)}┘=2, m≧(└√{square root over (r2)}┘−1)*MIN(n1,n2) when ┘√{square root over (r2)}┘ is >2 and even, and m≧n1+n2−1 when └√{square root over (r2)}┘=1. Each multicast connection is set up through such a three-stage network by use of only one switch in the middle stage.