Scheme illustrating the samples referred to in this work. Numbers in parentheses indicate the number of galaxies. From the main sample of dwarf central galaxies in TNG50-1 (white ellipse), we created a sample of AGN hosts (red ellipse). We also created three parent samples of non-AGN galaxies (gray ellipses), one sample of galaxies with no restriction (NR) on their properties, another of galaxies with the restriction of having gas (WG), and another of galaxies with the restriction of having black holes (WBH). Specific non-AGN control samples (pink, green, and blue boxes) are thus drawn from these parent samples, while the corresponding AGN samples (orange boxes) are drawn from the sample of active dwarf galaxies (red ellipse). Dashed lines indicate the pairing of a specific non-AGN control sample and its respective AGN samples, following the method described in Section 2.5. The colors of the boxes of control samples indicate the variables used as control, and correspond to the same colors used in Figure 4.