Abstract Single-cell RNA sequencing (scRNAseq) offers an unprecedented potential for scrutinizing complex biological systems at single cell resolution. One of the most important applications of scRNAseq is to cluster cells into groups of similar expression profiles, which allows unsupervised identification of novel cell subtypes. While many clustering algorithms have been tested towards this goal, graph-based algorithms appear to be the most effective, due to their ability to accommodate the sparsity of the data, as well as the complex topology of the cell population. An integral part of almost all such clustering methods is the construction of a k -nearest-neighbor (KNN) network, and the choice of k , implicitly or explicitly, can have a profound impact on the density distribution of the graph and the structure of the resulting clusters, as well as the resolution of clusters that one can successfully identify from the data. In this work, we propose a fairly simple but robust approach to estimate the best k for constructing the KNN graph while simultaneously identifying the optimal clustering structure from the graph. Our method, named scQcut , employs a topology-based criterion to guide the construction of KNN graph, and then applies an efficient modularity-based community discovery algorithm to predict robust cell clusters. The results obtained from applying scQcut on a large number of real and synthetic datasets demonstrated that scQcut —which does not require any user-tuned parameters—outperformed several popular state-of-the-art clustering methods in terms of clustering accuracy and the ability to correctly identify rare cell types. The promising results indicate that an accurate approximation of the parameter k , which determines the topology of the network, is a crucial element of a successful graph-based clustering method to recover the final community structure of the cell population. Availability ScQcut is written in both Matlab and Python and maybe be accessed through the links below. Matlab version: cs.utsa.edu/ jruan/scQcut Python version: https://github.com/mary77/scQcut Contact Jianhua.ruan@utsa.edu