Spike sorting algorithms aim at decomposing complex extracellular signals to independent events from single neurons in the electrode's vicinity. The decision about the actual number of active neurons is still an open issue, with sparsely firing neurons and background activity the most influencing factors. We introduce a graph-theoretical algorithmic procedure that successfully resolves this issue. Dimensionality reduction coupled with a modern, efficient and progressively executable clustering routine proved to achieve higher performance standards than popular spike sorting methods. Our method is validated extensively using simulated data for different levels of SNR.