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Many networks including the Internet, social networks, and biological relations are found to be naturally divided into communities of densely connected nodes, known as community structure. Since Newman's suggestion of using modularity as a measure to qualify the goodness of community structures, many efficient methods to maximize modularity have been proposed but without optimality guarantees. In this paper, we study exact and theoretically near-optimal algorithms for maximizing modularity. Indoi:10.1080/15427951.2014.950875 fatcat:snz3qfohnnbdvpcw7hrupwvjly