  Testing, tracking and tracing abilities have been identified as pivotal in
helping countries to safely reopen activities after the first wave of the
COVID-19 virus. Contact tracing apps give the unprecedented possibility to
reconstruct graphs of daily contacts, so the question is who should be tested?
As human contact networks are known to exhibit community structure, in this
paper we show that the Kemeny constant of a graph can be used to identify and
analyze bridges between communities in a graph. Our "Kemeny indicator" is the
change in Kemeny constant when a node or edge is removed from the graph. We
show that testing individuals who are associated with large values of the
Kemeny indicator can help in efficiently intercepting new virus outbreaks, when
they are still in their early stage. Extensive simulations provide promising
results in early identification and in blocking possible "super-spreaders"
links that transmit disease between different communities.
