Ayase has a very close relationship with her father, in fact he was the one who taught her everything she knew about swordsmanship, before Ikki had came along. This tight relationship is further displayed, when Ayase had gone from a shy girl, to one with fury in her eyes, after she had mistakenly thought that Ikki had called her father a bad swordsman. In the novel, they showed a more casual relationship to each other, as seen when Kaito teased her love life and she responded by a strike with a lament to beat him to coma again.
Ayase has great admiration for Ikki, as a fellow swordsman, as she sought his help in swordsmanship, when she had gone into a slump, when her teacher was injured. Ayase has stated that she is not romantically interested in Ikki, to Stella, during her training with Ikki at an outdoor pool. Ayase seems to also have respect for Ikki and his undying will to become the best.
Ayase is able to first have a true interaction with Stella, during her training time at the pool side after Ikki takes his leave. She is able to convince Stella to talk openly about her relationship with Ikki, and even giving advice on what she should do with Ikki, as she knew Ikki wouldn't hate Stella for pushing their relationship.
Ayase has a friendly relationship with Yuuri having a friendly conversation about Ikki.
Ayase has shown to absolutely hate, Kuraudo, so much so that Ikki saw a killing intent in Ayase's eyes the moment she had looked at him. Her hatred for Kuraudo was so intense that she had to bite her bottom lip just to keep from losing her temper around him.