  Connectivity of wireless sensor networks (WSNs) is a fundamental global
property expected to be maintained even though some sensor nodes are at fault.
In this paper, we investigate the connectivity of random geometric graphs
(RGGs) in the node fault model as an abstract model of ad hoc WSNs with
unreliable nodes. In the model, each node is assumed to be stochastically at
fault, i.e., removed from a graph. As a measure of reliability, the network
breakdown probability is then defined as the average probability that a
resulting survival graph is disconnected over RGGs. We examine RGGs with
general connection functions as an extension of a conventional RGG model and
provide two mathematical analyses: the asymptotic analysis for infinite RGGs
that reveals the phase transition thresholds of connectivity, and the
non-asymptotic analysis for finite RGGs that provides a useful approximation
formula. Those analyses are supported by numerical simulations in the Rayleigh
SISO model reflecting a practical wireless channel.
