Graph cut segmentation provides a platform to analyze images through a global segmentation strategy, and as a result of this, it has gained a wider acceptability in many interactive and automatic segmentation fields of application, such as the medical field. The graph cut energy function has a parameter that is tuned to ensure that the output is neither oversegmented (shrink bias) nor undersegmented. Models have been proposed in literature towards the improvement of graph cut segmentation, in the context of interactive and automatic cell segmentation. Along this line of research, the graph cut parameter has been leveraged, while in some instances, it has been ignored. Therefore, in this work, the relevance of graph cut parameter on both interactive and automatic cell segmentation is investigated. Statistical analysis, based on F1 score, of three publicly available datasets of cells, suggests that the graph cut parameter plays a significant role in improving the segmentation accuracy of the interactive graph cut than the automatic graph cut.