  The study of percolation phenomena has various applications ranging from
social networks or materials science to quantum information. The most common
percolation models are bond- or site-percolation for which the Newman-Ziff
algorithm enables an efficient simulation. Here, we consider several
non-standard percolation models that appear in the context of measurement-based
photonic quantum computing with so-called graph states and fusion networks. The
associated percolation thresholds determine the tolerance to photon loss in
such systems and we develop modifications of the Newman-Ziff algorithm to
perform the corresponding percolation simulation efficiently. We demonstrate
our algorithms by using them to characterize exemplary fusion networks and
graph states. The used source code is provided as an open-source repository.
