Pearson correlation p-values plot which method better adjusted my p-values BH or BY? help me understand

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I'm working on DEG dataset and I've done Pearson correlation to prepare my dataset for downstream analysis (co-expression network), so this isn't an exploration phase. When I do pearson on R using Hmisc I get P and R values. I'm trying to use these p-values to make sure that the correlation value r is significant, but since I don't know anyway to correct for pearson bias, I went with p.adjust.

I will attach 3 images 1 for the native p-values, BY-adjusted p.values, and BH-adjusted p.values. Looking at BH and native, I don't think BH adjusted anything, the curve is still showing perfect gradual decrease from 1 to 0, there are no adjusted p.values. While with BY, there is a noticeable new curve at 1 showing the adjusted values that were probably considered significant earlier.

The reason why I originally wanted to go with BY is because it assumes that the two correlated variables regulate or dependent on each other, which fits this biological concept.

Is my reasoning correct?

pearson native p-values

BH-adjusted p-values

BY-adjusted p-values

I tried reading about the expected plots for p-values, and other stackoverflow prior questions about this, unfortunately non-exactly addressed my question. I would love to get a more tailored response to my case in this question.

Thank you.

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