Spike sorting is a computational process that extracts firing times of single neurons from local electrical field recordings, a challenging task due to nonstationarity and dense overlap in electrical fields. The Kilosort framework has been developed to address this issue, with Kilosort4 being the latest version that significantly improves performance through graph-based clustering algorithms. This paper describes the algorithmic steps in Kilosort, including template deconvolution and graph-based clustering, and reports on its performance through realistic simulations. The core of Kilosort4 is a graph-based clustering algorithm that combines modularity optimization with a merging tree strategy to handle small clusters and improve processing speed. The algorithm was tested on various simulated conditions, showing superior performance compared to other algorithms, especially in high drift conditions. The results demonstrate that Kilosort4 can correctly identify neurons with low amplitudes and small spatial extents, making it a powerful tool for spike sorting in neuroscience research.Spike sorting is a computational process that extracts firing times of single neurons from local electrical field recordings, a challenging task due to nonstationarity and dense overlap in electrical fields. The Kilosort framework has been developed to address this issue, with Kilosort4 being the latest version that significantly improves performance through graph-based clustering algorithms. This paper describes the algorithmic steps in Kilosort, including template deconvolution and graph-based clustering, and reports on its performance through realistic simulations. The core of Kilosort4 is a graph-based clustering algorithm that combines modularity optimization with a merging tree strategy to handle small clusters and improve processing speed. The algorithm was tested on various simulated conditions, showing superior performance compared to other algorithms, especially in high drift conditions. The results demonstrate that Kilosort4 can correctly identify neurons with low amplitudes and small spatial extents, making it a powerful tool for spike sorting in neuroscience research.