Identifying and visualizing transcriptionally similar cells is instrumental for accurate exploration of the cellular diversity revealed by single-cell transcriptomics. However, widely used clustering and visualization algorithms produce a fixed number of cell clusters. A fixed clustering 'resolution' hampers our ability to identify and visualize echelons of cell states. We developed TooManyCells, a suite of graph-based algorithms for efficient and unbiased identification and visualization of cell clades. TooManyCells introduces a visualization model built on a concept intentionally orthogonal to dimensionality-reduction methods. TooManyCells is also equipped with an efficient matrix-free divisive hierarchical spectral clustering different from prevalent single-resolution clustering methods. TooManyCells enables multiresolution and multifaceted exploration of single-cell clades. An advantage of this paradigm is the immediate detection of rare and common populations that outperforms popular clustering and visualization algorithms, as demonstrated using existing single-cell transcriptomic data sets and new data modeling drug-resistance acquisition in leukemic T cells.