Single-cell RNA sequencing (scRNA-seq) technology provides the possibility to study cell heterogeneity and cell development on the resolution of individual cells. Arguably, three of the most important computational targets on scRNA-seq data analysis are data visualization, cell clustering and trajectory inference. Although a substantial number of algorithms have been developed, most of them do not treat the three targets in a systematic or consistent manner. In this article, we propose an efficient scRNA-seq analysis framework, which accomplishes the three targets consistently by non-uniform ε-neighborhood (NEN) network. First, a network is generated by our NEN method, which combines the advantages of both k-nearest neighbors (KNN) and ε-neighborhood (EN) to represent the manifold that data points reside in gene space. Then from such a network, we use its layout, its community and further its shortest path to achieve the purpose of scRNA-seq data visualization, clustering and trajectory inference. The results on both synthetic and real datasets indicate that our NEN method not only can visually provide the global topological structure of a dataset accurately compared with t-SNE (t-Distributed Stochastic Neighbor Embedding) and UMAP (Uniform Manifold Approximation and Projection), but also has superior performances on clustering and pseudotime ordering of cells over the existing approaches. This analysis method has been made into a python package called ccnet and is freely available at https://github.com/Just-Jia/ccNet. Supplementary data are available at Bioinformatics online.