Amaguji

Amaguji is the slash ship between Rantaro Amami and Korekiyo Shinguji from the Danganronpa fandom.

Canon
The two have very little interaction in the canon main plot, with the only one being when Korekiyo asks Rantaro how he wants to accomplish ending the killing game. However, they have more interactions in the bonus content.

During his first Free Time Event with Kaede, if the player chooses to talk about Kiyo, Rantaro tells Kaede that Korekiyo has a strong personality, but if she takes the time to speak with him she'll understand him. In addition, he emphasizes that Korekiyo is a calm person who seems to be a clever type.

The two also have two events together in the bonus mode, Ultimate Talent Development Plan. In these events, they bond over both of them travelling a lot, their knowledge about various cultures and having sisters who are important to them.

Fanon
The two are shipped together mostly as a result of the similarities between them that are pointed out in the Ultimate Talent Development Plan, with both of them having sisters who are important to them, travelling a lot, and possessing knowledge about various cultures - Rantaro as a result of travelling and Korekiyo as a result of being an anthropologist.

Fandom
AO3