In "Rikki-Tikki-Tavi," what is the relationship between Nag and Nagaina?

Rikki-Tikki-Tavi, or just Rikki-tikki as he is called throughout the story, is a mongoose in the eponymous story that is collected in Kipling's The Jungle Book. A mongoose is similar to a weasel, and they have a reputation as snake-killers. In this story, Rikki-tikki is pitted against Nag and Nagaina, a pair of cobras that are set on terrorizing the garden where Rikki-tikki and the other animals live, and ultimately driving off the human family that has adopted Rikki-tikki by killing their son, Teddy.
Shortly after she is introduced (via attempting to kill Rikki-tikki by sneaking up behind him), Nagaina is mentioned as being Nag's wife, and later his widow after Rikki-tikki kills Nag first. The cobras are shown to be equally cruel, vindictive and committed to the deaths of either Rikki-tikki or Teddy, and Rikki-tikki's fight with Nagaina is ultimately the more violent one because she forces him to fight her underground, where she has the advantage. Nevertheless, Rikki-tikki kills her as well, and the story concludes.