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This brief presents readers with a summary of classic, modern, and state-of-the-art methods for discovering the roles of entities in networks (including social networks) that range from small to large-scale. It classifies methods by their mathematical underpinning, whether they are driven by implications about entity behaviors in system, or if they are purely data driven. The brief also discusses when and how each method should be applied, and discusses some outstanding challenges toward the development of future role mining methods of each type.