  We introduce the concept of boundaries of a complex network as the set of
nodes at distance larger than the mean distance from a given node in the
network. We study the statistical properties of the boundaries nodes of complex
networks. We find that for both Erd\"{o}s-R\'{e}nyi and scale-free model
networks, as well as for several real networks, the boundaries have fractal
properties. In particular, the number of boundaries nodes {\it B} follows a
power-law probability density function which scales as $B^{-2}$. The clusters
formed by the boundary nodes are fractals with a fractal dimension $d_{f}
\approx 2$. We present analytical and numerical evidence supporting these
results for a broad class of networks. Our findings imply potential
applications for epidemic spreading.
