  Suppose that a cascade (e.g., an epidemic) spreads on an unknown graph, and
only the infection times of vertices are observed. What can be learned about
the graph from the infection times caused by multiple distinct cascades? Most
of the literature on this topic focuses on the task of recovering the entire
graph, which requires $\Omega ( \log n)$ cascades for an $n$-vertex bounded
degree graph. Here we ask a different question: can the important parts of the
graph be estimated from just a few (i.e., constant number) of cascades, even as
$n$ grows large?
  In this work, we focus on identifying super-spreaders (i.e., high-degree
vertices) from infection times caused by a Susceptible-Infected process on a
graph. Our first main result shows that vertices of degree greater than
$n^{3/4}$ can indeed be estimated from a constant number of cascades. Our
algorithm for doing so leverages a novel connection between vertex degrees and
the second derivative of the cumulative infection curve. Conversely, we show
that estimating vertices of degree smaller than $n^{1/2}$ requires at least
$\log(n) / \log \log (n)$ cascades. Surprisingly, this matches (up to $\log
\log n$ factors) the number of cascades needed to learn the \emph{entire} graph
if it is a tree.
