Single-cell RNA sequencing (scRNA-seq) data analysis faces numerous challenges, including high sparsity, a high-dimensional feature space, and biological noise. These challenges hinder downstream analysis, necessitating the use of feature selection methods to identify informative genes, and reduce data dimensionality. However, existing methods for selecting highly variable genes (HVGs) exhibit limited overlap and inconsistent clustering performance across benchmark datasets. Moreover, these methods often struggle to accurately select HVGs from fine-resolution scRNA-seq datasets and minority cell types, which are more difficult to distinguish, raising concerns about the reliability of their results. To overcome these limitations, we propose a novel feature selection framework for scRNA-seq data called Mcadet. Mcadet integrates Multiple Correspondence Analysis (MCA), graph-based community detection, and a novel statistical testing approach. To assess the effectiveness of Mcadet, we conducted extensive evaluations using both simulated and real-world data, employing unbiased metrics for comparison. Our results demonstrate the superior performance of Mcadet in the selection of HVGs in scenarios involving fine-resolution scRNA-seq datasets and datasets containing minority cell populations. Overall, we demonstrate that Mcadet enhances the reliability of selected HVGs, although the impact of HVG selection on various downstream analyses varies and needs to be further investigated.