  In this paper, we study correlation clustering under fairness constraints.
Fair variants of $k$-median and $k$-center clustering have been studied
recently, and approximation algorithms using a notion called fairlet
decomposition have been proposed. We obtain approximation algorithms for fair
correlation clustering under several important types of fairness constraints.
  Our results hinge on obtaining a fairlet decomposition for correlation
clustering by introducing a novel combinatorial optimization problem. We define
a fairlet decomposition with cost similar to the $k$-median cost and this
allows us to obtain approximation algorithms for a wide range of fairness
constraints.
  We complement our theoretical results with an in-depth analysis of our
algorithms on real graphs where we show that fair solutions to correlation
clustering can be obtained with limited increase in cost compared to the
state-of-the-art (unfair) algorithms.
