  In the graph shotgun assembly problem, we are given the balls of radius $r$
around each vertex of a graph and asked to reconstruct the graph. We study the
shotgun assembly of the Erd\H{o}s-R\'enyi random graph $\mathcal G(n,p)$ from a
wide range of values of $r$. We determine the threshold for reconstructibility
for each $r\geq 3$, extending and improving substantially on results of Mossel
and Ross for $r=3$. For $r=2$, we give upper and lower bounds that improve on
results of Gaudio and Mossel by polynomial factors. We also give a sharpening
of a result of Huang and Tikhomirov for $r=1$.
