So... is Inugami-san to Nekoyama-san finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 27, 2014
Manga finished: February 18, 2017
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Inugami-san to Nekoyama-san is a lighthearted comedy about the blossoming relationship between two high school girls, Yachiyo Inugami and Suzu Nekoyama.
Inugami, a very outgoing and energetic girl who loves cats, finds herself inexplicably drawn to the shy and introverted Nekoyama, who loves dogs.
Their contrasting personalities create a fun dynamic as Inugami tries to win Nekoyama's affection, often leading to comical misunderstandings and over-the-top reactions.
As their bond grows, they are joined by other quirky characters, like Mikine Nezu, and become involved in the school's "biology" club, adding more layers of humorous interactions to their everyday lives.
The anime focuses on the humorous and heartwarming journey of these girls as they navigate their unique friendship and the challenges of high school life, all while exploring their contrasting interests and personalities.