  In this paper we study the problem of correlation clustering under fairness
constraints. In the classic correlation clustering problem, we are given a
complete graph where each edge is labeled positive or negative. The goal is to
obtain a clustering of the vertices that minimizes disagreements -- the number
of negative edges trapped inside a cluster plus positive edges between
different clusters.
  We consider two variations of fairness constraint for the problem of
correlation clustering where each node has a color, and the goal is to form
clusters that do not over-represent vertices of any color.
  The first variant aims to generate clusters with minimum disagreements, where
the distribution of a feature (e.g. gender) in each cluster is same as the
global distribution. For the case of two colors when the desired ratio of the
number of colors in each cluster is $1:p$, we get
$\mathcal{O}(p^2)$-approximation algorithm. Our algorithm could be extended to
the case of multiple colors. We prove this problem is NP-hard.
  The second variant considers relative upper and lower bounds on the number of
nodes of any color in a cluster. The goal is to avoid violating upper and lower
bounds corresponding to each color in each cluster while minimizing the total
number of disagreements. Along with our theoretical results, we show the
effectiveness of our algorithm to generate fair clusters by empirical
evaluation on real world data sets.
