On the Capacity of Fractal D2D Social Networks with Hierarchical Communications

The maximum capacity of fractal D2D (device-to-device) social networks with both direct and hierarchical communications is studied in this paper. Specifically, the are characterized by connection self-similarity. Firstly, for a network communications, it proved that $ \Theta\left(\frac{1}{\sqrt{n\log n}}\right) if user communicates one his/her contacts randomly, where n denotes total number users network, can reach up to \Theta\left(\frac{1}{\log n}\right) any pair distance d communicate according probability proportion d^{-\beta} $. Secondly, since might get touch others without connections through inter-connected multiple users, these as well, related further derived. Our results show mainly affected correlation exponent $\epsilon$ structure. reduced proportional \frac{1}{{\log n}} 2<\epsilon<3 $, while reduction coefficient \frac{1}{n} \epsilon>3