Recent graph-based face clustering methods predict the connectivity of enormous edges, including false positive edges that link nodes with different classes. However, those false positive edges, which connect negative node pairs, have the risk of integration of different clusters when their connectivity is incorrectly estimated. This paper proposes a novel face clustering method to address this problem. The proposed clustering method employs density-based clustering, which maintains edges that have higher density. For this purpose, we propose a reliable density estimation algorithm based on local connectivity between K nearest neighbors (KNN). We effectively exclude negative pairs from the KNN graph based on the reliable density while maintaining sufficient positive pairs. Furthermore, we develop a pairwise connectivity estimation network to predict the connectivity of the selected edges. Experimental results demonstrate that the proposed clustering method significantly outperforms the state-of-the-art clustering methods on large-scale face clustering datasets and fashion image clustering datasets. Our code is available at https://github.com/illian01/LCE-PCENet