  We study the effect of the quality and quantity of side information on the
recovery of a hidden community of size $K=o(n)$ in a graph of size $n$. Side
information for each node in the graph is modeled by a random vector with the
following features: either the dimension of the vector is allowed to vary with
$n$, while log-likelihood ratio (LLR) of each component with respect to the
node label is fixed, or the LLR is allowed to vary and the vector dimension is
fixed. These two models represent the variation in quality and quantity of side
information. Under maximum likelihood detection, we calculate tight necessary
and sufficient conditions for exact recovery of the labels. We demonstrate how
side information needs to evolve with $n$ in terms of either its quantity, or
quality, to improve the exact recovery threshold. A similar set of results are
obtained for weak recovery. Under belief propagation, tight necessary and
sufficient conditions for weak recovery are calculated when the LLRs are
constant, and sufficient conditions when the LLRs vary with $n$. Moreover, we
design and analyze a local voting procedure using side information that can
achieve exact recovery when applied after belief propagation. The results for
belief propagation are validated via simulations on finite synthetic data-sets,
showing that the asymptotic results of this paper can also shed light on the
performance at finite $n$.
