  In community detection, the exact recovery of communities (clusters) has been
mainly investigated under the general stochastic block model with edges drawn
from Bernoulli distributions. This paper considers the exact recovery of
communities in a complete graph in which the graph edges are drawn from either
a set of Gaussian distributions with community-dependent means and variances,
or a set of exponential distributions with community-dependent means. For each
case, we introduce a new semi-metric that describes sufficient and necessary
conditions of exact recovery. The necessary and sufficient conditions are
asymptotically tight. The analysis is also extended to incomplete, fully
connected weighted graphs.
