Graph clustering and graph outlier detection have been studied extensively on plain graphs, with various applications. Recently, algorithms have been extended to graphs with attributes as often observed in the real-world. However, all of these techniques fail to incorporate the user preference into graph mining, and thus, lack the ability to steer algorithms to more interesting parts of the attributed graph. In this work, we overcome this limitation and introduce a novel user-oriented approach for mining attributed graphs. The key aspect of our approach is to infer user preference by the so-called focus attributes through a set of user-provided exemplar nodes. In this new problem setting, clusters and outliers are then simultaneously mined according to this user preference. Specifically, our FocusCO algorithm identifies the focus, extracts focused clusters and detects outliers. Moreover, FocusCO scales well with graph size, since we perform a local clustering of interest to the user rather than global partitioning of the entire graph. We show the effectiveness and scalability of our method on synthetic and real-world graphs, as compared to both existing graph clustering and outlier detection approaches.