  The aim of this paper is to analyse the evolution of the COVID-19 pandemic in
Rio Grande do Sul by applying graph-theoretical tools, particularly spectral
clustering techniques, on weighted graphs defined on the set of 167
municipalities in the state with population 10,000 or more, which are based on
data provided by government agencies and other sources. To respond to this
outbreak, the state has adopted a system by which pre-determined regions are
assigned flags on a weekly basis, and different measures go into effect
according to the flag assigned. Our results suggest that considering a flexible
approach to the regions themselves might be a useful additional tool to give
more leeway to cities with lower incidence rates, while keeping the focus on
public safety. Moreover, simulations show the dampening effect of isolation on
the dissemination of the disease.
