What a fun question!
There are many similarities between the character Hamlet and Charlie, the protagonist in The Perks of Being a Wallflower. For one, both characters have strong internal thoughts that drive their stories. In Hamlet, this takes the form of a number of soliloquies (think, "To be or not to be..."), while Charlie essentially "thinks" his entire novel, as it is written in letters from him to an unknown recipient. In allowing the audience to "see" the protagonists' thoughts so clearly, both Shakespeare and Stephen Chbosky give us deep insight into the personal turmoil of their lead characters.
Family is another important theme in both texts. In Hamlet, the entire story is driven by Hamlet's father's murder and his mother's subsequent marriage to his uncle. In The Perks of Being a Wallflower, Charlie's relationship with his parents and his Aunt Helen are vital parts of the story.
The difference, however, lies with how much the reader knows about the "sins" of the protagonists' family...
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