Quadrants

A piece of fan art, by Special-Sari, that helps illustrate the concept

Quadrants are a concept from Homestuck. Basically, quadrants are four different types of romance that a troll (a type of alien in the series) can experience. Each form has an associated color and card suit. The "red" relationship revolve around pity while the "black" one revolve around hate. It has also been stated moirallegiance and auspisticism more revolve around platonic emotions. Humans are stated to only be able to experience matespritship. 
Matespritship (♥)
As stated before, this is the one form of quadrant romance humans can experience. The partners feel affection for each other. However because troll culture, this form of romance can end up becoming violent. John's Dad and Rose's Mom are cited as an example. 
Moirallegiance (♦) 
Moirallegiance occur between a moirail and their partner. In this relationship, the moirail is watched over. Andrew Hussie, the creator of Homestuck, has stated the purpose of this relationship "is to pacify a partner who is dangerous" and "[its] not all about being platonic soul bros forever". The example given is Equius and Nepeta.  
Auspisticism (♣)
Auspitsticism involves three people instead of two. The auspistice acts as mediator that keeps a relationship between two partners functional. It has been shown an auspistice can be the only one feeling the emotions associated with this relationship and not the couple themselves. However, the comic has yet to say whether this is the norm or not. The example given is Kanaya mediating Vriska and Tavros' relationship.
Kismesissitude (♠)
Kismesissitude is based around mutual hatred and attraction at the same time. Despite the hate aspect, the partners usually have to respect each other to some degree for the relationship to last. The trolls discourage killing or defeating your mate since that would mean the end of the relationship. Jack Noir and the Black Queen is cited as an example.
Quadrant Vacillation
However, it is not uncommon for trolls for relationships for "flicker" between multiple quadrants, which is known as "Quadrant Vacillation". This usually is in the form of the Matespirt / Kismesis Double Reacharound or Group Vacillation. In MKDR, one partner experiences "red" feelings to a partner experiencing "black" ones. Either one partner has to change their feelings toward the other or an auspistice intervenes to is needed to keep the relationship stable. In Group Vacillation, trolls, who have a polygamous society, form multiple relationships and the resulting web of relations feature both "red" and "black" relationships.

References:

http://mspaintadventures.wikia.com/wiki/Quadrants
http://www.mspaforums.com/showthread.php?32390&p=4173696#post4173696