Nekomaru is close to Akane due to their desire to improve themselves physically. A Special Time Event in Chapter 3 reveals that Nekomaru has been doing "it" to Akane - giving massages.
Nekomaru, after Peko's execution, decided to guard the third island's entrance, due to being worried that Akane would do something reckless. She indeed does by challenging Monokuma to a battle. The host attempts to punish her with a shot from a bazooka for breaking the rules against the violence against the headmaster. However, Nekomaru stands in the way, taking the shot for her and saving her life.
She was the most shocked to discover that he was a robot and was really depressed about his death, never saying thank you to him because he always defended her. This led to Kazuichi Souda to use some of Nekomaru's remains to create a miniature version of himself to cheer her up.
During their time at Hope's Peak Academy, Akane and Nekomaru would often fight, Nekomaru considering it training, but Akane considering it battle. The two were rather close despite their constant fighting.
- “Akane...Fuyuhiko has finally come back to us. You better not do anything reckless... I can't stand...the thought of losing someone...any longer.”
- —Nekomaru telling Akane not to do anything reckless so he won't lose her, in Chapter 3 of Danganronpa 2.
- “That stupid fool! No...I'm the one who was the fool... It was my mistake to not keep my eyes on her! Tch...! As a team manager, I should've had a proper grasp of my athlete's private life... Dammiiiiiiit! This failure will haunt me for the rest of my life, or my name isn't NEKOMARU NIDAIIIIIIII!!!!”
- —Nekomaru blaming himself for Akane acting recklessly by fighting Monokuma.
- Akane – “N-Nekomaru...Why did you...s-save...?”
- Nekomaru – “Ha... Isn't it obvious...? Supporting their athletes....is...a manager's duty. H-However... Wh-What a shame... For someone like NEKOMARU NIDAI...to... It was just a little shot from a bazooka... I really am the worst... Heh...hehe...hah... Akane... The time I've spent with you...i-it...it wasn't so bad... Don't...die...Akane...”
- — Akane and Nekomaru's dialogue before the latter's first "death".
- “There's no need to worry about worryin'! I know coach Nekomaru is a monstrous guy. There's no way he's gonna die from somethin' like that... There's no doubt! Nekomaru is definitely gonna come back! S-So...when that happens...I'll make sure...I apologize to him. Cause I was too weak, and I caused him trouble... So when he comes back... I'll make sure...to say I'm sorry.”
- —Akane wants to apologize to Nekomaru for nearly getting him killed.
- “When I think about Nekomaru...it's like...my knees start shakin'... That's weird... There's no way...I've got that kinda weakness. It'd prolly go away if I battled a strong dude, but Nekomaru's not here...”
- —Akane about her feelings to Nekomaru.
- “I'm sure you don't want to hear this, since I caused a similar incident... And I already know that a guy like me has no right to say this to you but... But...when I look at you, I just have to say something...! You don't need to act so stubborn, you know? 'Cause...I know what you're going through. The only reason you're standing here right now...is because someone sacrificed himself for you... You feel guilty about that. Isn't that right? So you don't want to be honest about it, huh... Well, I understand that feeling too... But like he said, it's better to just be alive... It might hurt to look at his painful appearance right now... But you're much better off because at least he's still alive! I mean...for me... ... S-Sorry... Right now...I feel very grateful to her... But I can't tell her that anymore. But you're different. So... Make sure you tell him how grateful you are...”
- —Fuyuhiko Kuzuryu giving Akane an advice about Nekomaru in Chapter 4.
- “Why is Nekomaru...? Why did he have to die...again? Dammit... I never paid you back... I never paid you back...for your help last time! WAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHHHHHHHHHHHHH!”
- —Akane crying after Nekomaru's death.
- “I'm here today...because coach Nekomaru risked his life...to protect me... I'm gonna be the one who avenges him! I'll definitely find out who the killer is!”
- —Akane motivated to avenge Nekomaru's death by finding out his killer.
The ship sailed as a result of their canon interactions, with the two often training together. The very suggestive special time event where it was revealed that the "it" that Nekomaru has been going to Akane were his massages further fueled the ship. The fact that their most important interaction is with each other also helped. So did both times when Akane mourned Nekomaru's death.
It is the most written ship for both of them on Archive of Our Own. Fan fictions tend to portray their relationship the same way the canon did, with them being training partners. Some however include an actual romantic relationship between the two.