On the Capacity of Fractal Wireless Networks With Direct Social Interactions

Abstract

The capacity of a fractal wireless network with direct social interactions is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution $P(k)$, and we capture the connection feature between two nodes with degree $k_1$ and $k_2$ by a joint probability distribution $P(k_1,k_2)$. It is proved that if the source node communicates with one of its direct contacts randomly, the maximum capacity is consistent with the classical result $\Theta \left(\frac{1}{\sqrt{n\log n}}\right)$ achieved by Kumar \cite{Gupta2000The}. On the other hand, if the two nodes with distance $d$ communicate according to the probability $d^{-\beta }$, the maximum capacity can reach up to $\Theta \left(\frac{1}{\log n}\right)$, which exhibits remarkable improvement compared with the well-known result in \cite{Gupta2000The}.

References in corpus (1)

• Scaling of degree correlations and the influence on diffusion in scale-free networks