  Bootstrap percolation in (random) graphs is a contagion dynamics among a set
of vertices with certain threshold levels. The process is started by a set of
initially infected vertices, and an initially uninfected vertex with threshold
$k$ gets infected as soon as the number of its infected neighbors exceeds $k$.
This process has been studied extensively in so called \textit{rank one}
models. These models can generate random graphs with heavy-tailed degree
sequences but they are not capable of clustering. In this paper, we treat a
class of random graphs of unbounded rank which allow for extensive clustering.
Our main result determines the final fraction of infected vertices as the fixed
point of a non-linear operator defined on a suitable function space. We propose
an algorithm that facilitates neural networks to calculate this fixed point
efficiently. We further derive criteria based on the Fr\'echet derivative of
the operator that allows one to determine whether small infections spread
through the entire graph or rather stay local.
