A new spectral method is proposed for community detection in large dense heterogeneous networks. We theoretically support and analyze an approach based on a novel ``$ \alpha $-regularization" of the modularity matrix. We provide a consistent estimator for the choice of $\alpha$ inducing the most favorable community detection in worst case scenarios. We further prove that spectral clustering ought to be performed on a $1-\alpha$ regularization of the dominant eigenvectors (rather than on the eigenvectors themselves) to compensate for biases due to degree heterogeneity. Our clustering method is shown to be very promising on real world networks with competitive performances versus state-of-the-art spectral techniques developed for sparse homogeneous networks.