When Harry Potter arrives at Hogwarts School of Witchcraft and Wizardry, he is a young boy who has never had friends or been part of a community. He has grown up with an aunt, uncle and cousin who despised him, and his cousin's bullying ways ensured that Harry was never able to make any friends at the school which they both attended.
Becoming friends with Ron Weasley and Hermione Granger, thereby gaining the sense of being part of a community, is one of the most significant changes that Harry undergoes when he arrives at Hogwarts. I would argue that this sense of community is far more important to Harry than the fact that he is a wizard and is now learning all sorts of magic. This notion of being part of a "figure of three" changes Harry's life in all sorts of ways. Friendship is clearly the most important community-related theme in this great novel.
It is not only in the case of Harry, Ron and Hermione that Rowling showcases the power of community in sets of three. Harry's nemesis at school, Draco Malfoy, is never seen without his two close friends, who are known as Crabbe and Goyle.
Having lived an alienated childhood without friends or caring family members around him, it makes perfect sense that his newfound sense of community would be of such critical importance to Harry.
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