  Finding influential spreaders of information and disease in networks is an
important theoretical problem, and one of considerable recent interest. It has
been almost exclusively formulated as a node-ranking problem -- methods for
identifying influential spreaders rank nodes according to how influential they
are. In this work, we show that the ranking approach does not necessarily work:
the set of most influential nodes depends on the number of nodes in the set.
Therefore, the set of $n$ most important nodes to vaccinate does not need to
have any node in common with the set of $n+1$ most important nodes. We propose
a method for quantifying the extent and impact of this phenomenon, and show
that it is common in both empirical and model networks.
