  We propose a rate optimal estimator for the linear regression model on
network data with interacted (unobservable) individual effects. The estimator
achieves a faster rate of convergence $N$ compared to the standard estimators'
$\sqrt{N}$ rate and is efficient in cases that we discuss. We observe that the
individual effects alter the eigenvalue distribution of the data's matrix
representation in significant and distinctive ways. We subsequently offer a
correction for the \textit{ordinary least squares}' objective function to
attenuate the statistical noise that arises due to the individual effects, and
in some cases, completely eliminate it. The new estimator is asymptotically
normal and we provide a valid estimator for its asymptotic covariance matrix.
While this paper only considers models accounting for first-order interactions
between individual effects, our estimation procedure is naturally extendable to
higher-order interactions and more general specifications of the error terms.
