The onset of an early or extra period is fairly standard with any fast weight loss diet, particularly ketogenic diets.
I'm not a doctor or a science expert but hormones are ALL OVER weight related issues. Our hormone levels determine where we store our fat. There's a hormone called leptin that makes you feel full and one called grelin that signals hunger.
If you're severely under or overweight your hormones will be so out of balance your periods will often stop, and being overweight can both trigger and be caused by the condition PCOS (polycystic ovarian syndrome) which actually more often than not occurs in people with no cysts on their ovaries, just a big hormone imbalance.
We store hormones, particularly oestrogen, in our fat, meaning if we lose weight fast we can get hit by a rush of them, causing mood swings. It's also part of why overweight men sometimes get moobs.
Seratonin is a hormone, a feel-good one, and restricting protein on a low carb diet can often make people feel depressed. On a high protein ketogenic diet it can contribute to the positive, overactive feeling we get sometimes.
That's all I can remember offhand and nothing is a direct quote, just little bits I remember from here and there.