Undirected, high dimensional and sparse networks are frequently encountered in industrial applications. They contain rich knowledge regarding various useful patterns. Non-negative latent factor (NLF) models have proven to be effective and efficient in acquiring useful knowledge from asymmetric networks. However, they cannot correctly describe the symmetry of an undirected network. For addressing this issue, this work analyzes the NLF extraction processes on asymmetric and symmetric matrices respectively, thereby innovatively achieving the symmetric and non-negative latent factor (SNLF) models for undirected, high dimensional and sparse networks. The proposed SNLF models are equipped with a) high efficiency, b) non-negativity, and c) symmetry. Experimental results on real networks show that they are able to a) represent the symmetry of the target network rigorously; b) maintain the non-negativity of resulting latent factors; and c) achieve high computational efficiency when performing data analysis tasks as missing data estimation.