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• Integrating the item graphs into an adapted semi-supervised learning model. • The combination of global graph and local graphs achieves better performance. • Such combination will not introduce the instability of local models. Graph-based recommendation models work well for top-N recommender systems due to their capability to capture the potential relationships between entities. However, most of the existing methods only construct a single global item graph shared by all the users and regrettably ignore the diverse tastes between different user groups. Inspired by the success of local models for recommendation tasks, this paper provides the first attempt to investigate multiple local item graphs along with a global item graph for graph-based recommendation models. We argue that recommendation on global and local graphs outperforms that on a single global graph or multiple local graphs. Specifically, we propose a novel graph-based recommendation model named GLIMG (G lobal and L ocal I te M G raphs), which simultaneously captures both the global and local user tastes. By integrating the global and local graphs into an adapted semi-supervised learning model, users' preferences on items are propagated globally and locally. Extensive experimental results on real-world datasets show that our proposed method consistently outperforms the state-of-the-art counterparts on the top-N recommendation task. [ABSTRACT FROM AUTHOR]