  In wireless networks, the knowledge of nodal distances is essential for
several areas such as system configuration, performance analysis and protocol
design. In order to evaluate distance distributions in random networks, the
underlying nodal arrangement is almost universally taken to be an infinite
Poisson point process. While this assumption is valid in some cases, there are
also certain impracticalities to this model. For example, practical networks
are non-stationary, and the number of nodes in disjoint areas are not
independent. This paper considers a more realistic network model where a finite
number of nodes are uniformly randomly distributed in a general d-dimensional
ball of radius R and characterizes the distribution of Euclidean distances in
the system. The key result is that the probability density function of the
distance from the center of the network to its nth nearest neighbor follows a
generalized beta distribution. This finding is applied to study network
characteristics such as energy consumption, interference, outage and
connectivity.
