Parallel association rules mining is a noticeable problem in data mining. However, little work has been proposed to deal with three important issues: (1) less memory usage; (2) less communication, among the involved computers, over the network; and (3) load balance among computers. In this paper, we present a graph-based scheme to solve the parallel mining problem by applying independent groups (clusters of maximal cliques). To bring the three issues to a close, the purpose of the independent groups aims at dividing a database into several independent sub-databases, so each sub-database can be employed independently to perform mining algorithms. To emphasis the effectiveness of the graph-based scheme, we adopt the independent groups not only for maximal large itemsets mining but also for general large itemsets mining. The experimental results show that our scheme can improve the efficiency for parallel mining when the independent groups are well-organized and designed.