Covariance Neural Networks (VNNs) leverage the covariance matrix of user-item rating data to construct graph structures that enable effective graph convolutions for collaborative filtering. However, empirical covariance estimates often contain noisy correlations arising from limited or sparse data, which can degrade the stability and predictive accuracy of VNNs. This paper investigates how sparsification techniques applied to the covariance matrix can mitigate noise and improve model efficiency. We propose a flexible framework that performs thresholding, which removes edges with weights below a fixed cutoff, and stochastic sparsification, which randomly retains edges based on their strength, thereby adapting to both sparse and dense covariance patterns.