  k-connectivity of random graphs is a fundamental property indicating
reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of
sensor nodes with limited power resources are modeled by random graphs with
unreliable nodes, which is known as the node fault model. In this paper, we
investigate k-connectivity of random graphs in the node fault model by
evaluating the network breakdown probability, i.e., the disconnectivity
probability of random graphs after stochastic node removals. Using the notion
of a strongly typical set, we obtain universal asymptotic upper and lower
bounds of the network breakdown probability. The bounds are applicable both to
random graphs and to random geometric graphs. We then consider three
representative random graph ensembles: the Erdos-Renyi random graph as the
simplest case, the random intersection graph for WSNs with random key
predistribution schemes, and the random geometric graph as a model of WSNs
generated by random sensor node deployment. The bounds unveil the existence of
the phase transition of the network breakdown probability for those ensembles.
