  Given a graph $G$ whose edges are perfectly reliable and whose nodes each
operate independently with probability $p\in[0,1],$ the node reliability of $G$
is the probability that at least one node is operational and that the
operational nodes can all communicate in the subgraph that they induce; it is
the analogous node measure of robustness to the well studied
\textit{all-terminal reliability}, where the nodes are perfectly reliable but
the edges fail randomly. In sharp contrast to what is known about the roots of
the all-terminal reliability polynomial, we show that the node reliability
polynomial of any connected graph on at least three nodes has a nonreal
polynomial root, the collection of real roots of all node reliability
polynomials is unbounded, and the collection of complex roots of all node
reliability polynomials is dense in the entire complex plane.
