Abstract
The paper investigates the implementation of virtual networks on the SDN data plane, modeled by a graph of physical connections between network nodes. A virtual network is defined as a set of ordered host pairs (sender, receiver), and it is implemented by a set of host-host paths that uniquely determine the switch settings. It is shown that any set of host pairs can be implemented on a connected graph without the occurrence of an infinite transfer of packets in a loop and without duplicate paths when the host receives the same packet several times. However, undesired paths may occur when a host receives a packet that is not intended for this host. On the other hand, it is shown that in some cases, implementation without undesired paths inevitably leads to duplication or looping of packets. The question is posed: on which graph can any set of host pairs be implemented without looping, duplication and undesired paths? A sufficient condition is proposed and a hypothesis is put that this condition is also the necessary condition.
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