Quadrants

Troll culture is built around a set of extremely complicated relationships. As Karkat says to Vriska, trolls are driven by the two primary emotions, hate and pity. It seems like both of these are necessary in troll society, although most of their social system remains obscure. Known types of relationships include mating fondness, moirallegiance, black romance, and red romance

Black Romance
Given Karkat's comments in the aforementioned conversation, black romance is what a troll feels towards someone known as their kismesis. This is linked to hatred, and it is necessary that both parties feel hatred towards each other. It is unknown whether any of the revealed romances between troll characters fall under this category.

Moirallegiance
Moirallegiance is a process that occurs between a troll and their "moiral". It appears that moirallegiance is linked to pity the same way that black romance is linked to hate. Strangely enough, these seem to be completely different processes; Karkat implies that Vriska's moiral and kismesis would be different people.