  In cerebrovascular networks, some vertices are more connected to each other
than with the rest of the vasculature, defining a community structure. Here, we
introduce a class of model networks built by rewiring Random Regular Graphs,
which enables to reproduce this community structure and other topological
properties of cerebrovascular networks. We use these model networks to study
the global flow reduction induced by the removal of a single edge. We
analytically show that this global flow reduction can be expressed as a
function of the initial flow rate in the removed edge and of a topological
quantity, both of which display probability distributions following Cauchy
laws, i.e. with large tails. As a result, we show that the distribution of
blood flow reductions is strongly influenced by the community structure. In
particular, the probability of large flow reductions increases substantially
when the community structure is stronger, weakening the network resilience to
single capillary occlusions. We discuss the implications of these findings in
the context of Alzheimer's Disease, in which the importance of vascular
mechanisms, including capillary occlusions, is beginning to be uncovered.
