  We present a weighted estimator of the covariance and correlation in
bipartite complex systems with a double layer of heterogeneity. The advantage
provided by the weighted estimators lies in the fact that the unweighted sample
covariance and correlation can be shown to possess a bias. Indeed, such a bias
affects real bipartite systems, and, for example, we report its effects on two
empirical systems, one social and the other biological. On the contrary, our
newly proposed weighted estimators remove the bias and are better suited to
describe such systems.
