I am size, weight and power constrained so I can't install a router. All the arduino has to do is take some messages in and relay them on to the private network. The private network is just a network of arduinos and the traffic is very light.
The network structure is as follows.
My Server ----- > Arduino Ethernet -> Ethernet Shield ------ > Other Arduino Ethernet
I have a very low powered network switch that I can power off the 5V pin of the arduino ethernet but I would rather not do that as it takes up more space then I would like.