In the context of network theory a scale-free ideal network is a random network with a degree distribution following the scale-free ideal gas density distribution. These networks have the special property of reproducing the city-size distribution and electoral results unravelling the size distribution of social groups with information theory on complex networks, when a competitive cluster growth process is applied to the network. In models of scale-free ideal networks it is possible to demonstrate that Dunbar's number is the cause of the phenomenon known as the 'six degrees of separation' .
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