  We delve into the statistical properties of regions within complex networks
that are distant from vertices with high centralities, such as hubs or highly
connected clusters. These remote regions play a pivotal role in shaping the
asymptotic behaviours of various spreading processes and the features of
associated spectra. We investigate the probability distribution $P_{\geq m}(s)$
of the number $s$ of vertices located at distance $m$ or beyond from a randomly
chosen vertex in an undirected network. Earlier, this distribution and its
large $m$ asymptotics $1/s^2$ were obtained theoretically for undirected
uncorrelated networks [S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin,
Nucl. Phys. B 653 (2003) 307]. Employing numerical simulations and analysing
empirical data, we explore a wide range of real undirected networks and their
models, including trees and loopy networks, and reveal that the inverse square
law is valid even for networks with strong correlations. We observe this law in
the networks demonstrating the small-world effect and containing vertices with
degree $1$ (so-called leaves or dead ends). We find the specific classes of
networks for which this law is not valid. Such networks include the
finite-dimensional networks and the networks embedded in finite-dimensional
spaces. We notice that long chains of nodes in networks reduce the range of $m$
for which the inverse square law can be spotted. Interestingly, we detect such
long chains in the remote regions of the undirected projection of a large Web
domain.
