  We provide a general framework for computing lower-bounds on the sample
complexity of recovering the underlying graphs of Ising models, given i.i.d
samples. While there have been recent results for specific graph classes, these
involve fairly extensive technical arguments that are specialized to each
specific graph class. In contrast, we isolate two key graph-structural
ingredients that can then be used to specify sample complexity lower-bounds.
Presence of these structural properties makes the graph class hard to learn. We
derive corollaries of our main result that not only recover existing recent
results, but also provide lower bounds for novel graph classes not considered
previously. We also extend our framework to the random graph setting and derive
corollaries for Erd\H{o}s-R\'{e}nyi graphs in a certain dense setting.
