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Earthly Branch Relationship
Affinity Relationship (Attraction)
The affinity relationship of Earthly Branches is from the relative positions (in the sky) of Sun and Moon in an old calendar system.
Enmity Relationship (Fighting/Rejection)
Just like Stem relationship, the enmity relationship is from relative positions of the elements. Chinese considered "face to face" as the enmity relationship. Wood is in the east and faces Metal in the West. Water is in the north and faces Fire in the south. They are dislike each other, so they live in different places. Also, same genders reject each other which is natural.
There is an Enmity Relationship when the difference of two Branch sequences is six.