  Quarantining and contact tracing are popular ad hoc practices for mitigating
epidemic outbreaks. However, few mathematical theories are currently available
to asses the role of a network in the effectiveness of these practices. In this
paper, we study how the final size of an epidemic is influenced by the
procedure that combines contact tracing and quarantining on a network null
model: the configuration model.
  Namely, we suppose that infected vertices may self-quarantine and trace their
infector with a given success probability.
  A traced infector is, in turn, less likely to infect others. We show that the
effectiveness of such tracing process strongly depends on the network
structure. In contrast to previous findings, the tracing
  procedure is not necessarily more effective on networks with heterogeneous
degrees. We also show that network clustering influences the effectiveness of
the tracing process in a non-trivial way: depending on the infectiousness
parameter, contact tracing on clustered networks may either be more, or less
efficient than on network without clustering.
