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If this center-stage change is now faraway from the Clos network, m is diminished by 1, and we are left with a smaller Clos network. Within the context of a Clos network, each boy represents an ingress switch, and every lady represents an egress switch. In the worst case, n−1 other calls are active on the ingress change in question, and n−1 different calls are lively on the egress change in question. Each ingress stage crossbar switch has m outlets, and there are m middle stage crossbar switches. There are r egress stage switches, every with m inputs and n outputs. Let A be the number of how of assigning the j output calls to the m middle stage switches. This is the variety of instances in which the remaining m−j middle stage switches coincide with m−j of the i input calls, which is the variety of subsets containing m−j of those calls. Each middle stage change is linked exactly as soon as to every egress stage switch. Hence in the worst case, 2n−2 of the center stage switches are unable to hold the new call. A boy is alleged to know a girl if the corresponding ingress and egress switches carry the identical name.

A Clos network topology (diagrammed below) is parameterized by three integers n, m, and r: n represents the number of sources which feed into each of r ingress stage crossbar switches; each ingress stage crossbar swap has m shops; and there are m center stage crossbar switches. There is strictly one connection between every ingress stage switch and every middle stage swap. There are i input calls entering via the same ingress swap because the free input terminal to be connected, and there are j calls leaving the Clos network (output calls) via the identical egress change because the free output terminal to be connected. Each set of ok boys should know not less than k girls as a result of okay ingress switches are carrying k×n calls and these can’t be carried by lower than k egress switches. The theorem states that if each subset of k boys (for every okay such that zero ≤ okay ≤ r) between them know okay or extra women, then every boy could be paired off with a girl that he is aware of.

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