With the advancement of the high throughput single cell techniques, transcriptomics data generation at the single cell level becomes very easy. Analysis of this single cell expression values can reveal lots of unprecedented information about complex cellular heterogeneity and tissue composition. To date, different statistical methods are applied to analyze expression data at the cellular level, but there is still pretty much scope for the development of new bioinformatics tools. In this article, a graph theoretic clustering algorithm is proposed to identify cellular states from single cell gene expression data. The proposed algorithm first generates a shared nearest neighbor graph from the single cell RNA-seq dataset and then applies minimum spanning tree based clustering method to cluster the graph nodes. To compare our proposed algorithm’s performance with other unsupervised clustering methods, we used three real scRNA-seq datasets (human cancer cells, human embryonic cells and mouse embryonic cells). From the comparison result, it is evident that the proposed algorithm outperforms other standard single cell analysis methods.