The household does not appear to me to be a random colletion of relations. While the census doesn't state relationships, I'm fairly certain this is the case:
Elizabeth Stowe, a widow, is the head of the household which contained:
her son John, his new wife Margaret, and his children: Minerva, Harriet, Elinor, and Cynthia. her son Eliakim, his son Franklin her son Westly, his wife Hannah E, and their daughter Flora her son Apollos her son Harmon (?) her daughter Lucy Ann, with her husband Clark Rathbun (who she had married in the year), and her son? Charles Neal. In 1860, John, Margaret and their children are living in Hancock County. Eliakim and his family, and Westly and his family are living in Fulton County.