  We consider a random partition of the vertex set of an arbitrary graph that
can be sampled using loop-erased random walks stopped at a random independent
exponential time of parameter $q>0$, that we see as a tuning parameter.The
related random blocks tend to cluster nodes visited by the random walk on time
scale $1/q$. We explore the emerging macroscopic structure by analyzing 2-point
correlations. To this aim, it is defined an interaction potential between pair
of vertices, as the probability that they do not belong to the same block of
the random partition. This interaction potential can be seen as an affinity
measure for ``densely connected nodes'' and capture well-separated regions in
network models presenting non-homogeneous landscapes. In this spirit, we
compute this potential and its scaling limits on a complete graph and on a
non-homogeneous weighted version with community structures. For the latter
geometry we show a phase-transition for ``community detectability'' as a
function of the tuning parameter and the edge weights.
