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Networks with a very large number of nodes are known to suffer from scal- ability problems, influencing throughput, delay and other quality of service (QoS) pa- rameters. Mainly applicable to wireless sensor networks, this paper extends the work of (1) and aims to give some fundamental indications on a scalable and optimum (or near-optimum) structuring approach for large-scale wireless networks. Scalability and optimality will be defined w.r.t. various performance criteria, an example of which is the throughput per node in the network. Various laws known from different domains will be invoked to quantify the performance of a given topology; most notably, we will make use of the well-known Kumar's law, as well as less known Zipf's and other scaling laws. Optimum network structures are derived and discussed for a plethora of different scenarios, facilitating knowledgeable design guidelines for these types of networks.

Kumar’s, Zipf’s and other laws: how to structure a large-scale wireless network?