  Social networks and interactions in social media involve both positive and
negative relationships. Signed graphs capture both types of relationships:
positive edges correspond to pairs of "friends", and negative edges to pairs of
"foes". The {\em edge sign prediction problem}, which aims to predict whether
an interaction between a pair of nodes will be positive or negative, is an
important graph mining task for which many heuristics have recently been
proposed \cite{leskovec2010predicting,leskovec2010signed}.
  Motivated by social balance theory, we model the edge sign prediction problem
as a noisy correlation clustering problem with two clusters. We are allowed to
query each pair of nodes whether they belong to the same cluster or not, but
the answer to the query is corrupted with some probability $0<q<\frac{1}{2}$.
Let $c=\frac{1}{2}-q$ be the gap. We provide an algorithm that recovers the
clustering with high probability in the presence of noise for any constant gap
$c$ with $O(n^{1+\tfrac{1}{\log\log{n}}}\log{n})$ queries. Our algorithm uses
simple breadth first search as its main algorithmic primitive. Finally, we
provide a novel generalization to $k \geq 3$ clusters and prove that our
techniques can recover the clustering if the gap is constant in this
generalized setting.
