  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}.
