In the context of complex network systems, we model social networks with the property that there is certain degradation of the information flowing through the network. We analyze different kinds of networks, from regular lattices to random graphs. We define an average coordination degree for the network, which can be associated with a certain notion of efficiency. Assuming that there is a limit to the information a person may handle, we show that there exists a close relationship between the structure of the network and its maximum size.