Let's start by busting some astrological myths.

The direct nodes are rare.

It's commonly floated around that the nodes are direct only once or twice a month. The implication of this is that they are only direct for a day or two, and then go back to being retrograde. But the Moon's nodes are direct, on average, for as long, if not longer, than the time that Mercury is in retrograde every year. So let's do some math (I know, math is gross, but stick with me).

A compilation of direct nodes using Astrodienst Ephemeris
Astrodienst Ephemeris (located here so you can follow along). Midnight (00:00) UT time. Time frame covers 2005-2025. For personal use only, please do not redistribute without explicit written permission. 
Direct nodes compilation using the LUNA astrology ephemeris
LUNA Software for the direct nodes (12 pm / noon UTC time) Time frame covers 2005-2025. For personal use only, please do not redistribute without explicit written permission. 
Direct nodes in The New American Ephemeris compilation.
The New American Ephemeris for the 21st Century 2000-2100 at Midnight, Michelsen Memorial Edition direct nodes compilation. ET (Ephemeris time). Time frame covers 2005-2025. For personal use only, please do not redistribute without explicit written permission. 

Please don't let all the graphs freak you out! They are just to chart when the nodes were most and least direct from the years 2005-2025. A key is at the bottom of each. Yellow is the months that the nodes were most direct that year, orange is the second most direct month(s) of the year. Bright blue/green is the months the nodes were least direct out of the year, with the darker blue being the second most least direct months out of the year. Chart reads left to right, with years being vertical and months for the years being horizontal. Total days direct per year are at the rightmost side of each year, while total days direct per month are at the very bottom with average days per month. Total days direct from 2005-2025 are in the right hand corner beneath the row of total days direct per year.

On that note, if you are blue/yellow colorblind, please let me know and I can change the colors for you.

I was going to do another one or two sources/softwares, but after I got to three I thought it was a little overkill. The Astrodienst software has their free ephemeris here, for anyone who wants to follow along. They were also kind enough to send me a text file of more accurate dates. That file is not included in the compiled data above, because I wanted to have a free source that everyone could access and follow along to.

Some things I noticed:

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