This page outlines Katsuragi's relationship with characters in the Senran Kagura 3DS series.
Unnamed Mother and Father
Not much is talked about the relationship between Katsuragi and her parents, but it's implied in the games that their relationship is normal. In each game Katsuragi continues to work hard to become a powerful and respected shinobi in order to make amends with what her parents done in the past and to be able to reunite with them.
Katsuragi and Asuka seems to have a stable relationship. Asuka looks up to both Katsuragi and Ikaruga as her seniors and older sisters. Whenever Katsuragi interacts with Asuka, Katsuragi is seen sexually harassing her since she is an easy target. At times, Asuka doesn't appreciate it, but other times, she doesn't mind it.
Ikaruga is considered Katsuragi's closest friend out of everyone else she befriended. During the events of Spark! and a flashback sequence of the anime, their relationship was poor at the start, but as they got to know one another and realize how similar they are, they've became close friends to the point of being able to cooperate with one another fluently in battle. They both look after one another and comfort each other in case they need it. Just like Asuka, Katsuragi likes to sexually harass Ikaruga to help keep her relaxed, but sometimes, Ikaruga doesn't tolerate it.
Katsuragi and Yagyū seems to have a stable relationship. They don't interact with each other that much, but they both respect each other as comrades and friends. However, whenever Katsuragi is interacting with Hibari, there are times when Yagyū decides to threaten to harm Katsuragi if she does anything inappropriate to Hibari. There are other times when Yagyū just doesn't tolerate with Katsuragi's shenanigans at all. Basically, Yagyū keeps Katsuragi in check in case she goes too far.
Katsuragi and Hibari seems to have a stable relationship. Similar to Asuka, Hibari looks up to Katsuragi along with Ikaruga as her seniors and older sisters. They don't interact with one another individually but whenever they're with the others together, there are times where Katsuragi's shenanigans causes Hibari to be curious about them as she tries to either imitate them or she just goes along with it, causing Yagyū to be annoyed by Katsuragi.
Hikage is considered Katsuragi's closest rival and one of her closest friends. Throughout both arcs in Burst, Katsuragi tries her best to help Hikage develop her own emotions and understand the joy of fighting a good opponent. By the end, she was able to do so. In Deep Crimson, their relationship has grown further with Hikage being able to help Katsuragi with her troubles as she continues to develop more emotions. In general, whenever Katsuragi is up to something mischievous, Hikage doesn't tolerate it, but not to the same extent as Yagyū.