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Many different approaches have been proposed for the challenging problem of visually analyzing large networks. Clustering is one of the most promising. In this paper we propose a new goal for clustering that is especially tailored to hybrid-visualization tools. Namely, that of producing both intra-cluster graphs and inter-cluster graph that are suitable for highly-readable visualizations within different representation conventions. We formalize this concept in the (X,Y)-clustering framework, where Y is the class that defines the desired topological properties of intra-cluster graphs and X is the class that defines the desired topological properties of the inter-cluster graph. By exploiting this approach hybrid-visualization tools can effectively combine different node-link and matrix-based representations, allowing the users to interactively explore the graph by expansion/contraction of clusters without loosing their mental map. As a proof of concept, we describe the system VHYXY (Visual Hybrid (X,Y)-clustering) that integrates our techniques and we present the results of case studies to the visual analysis of co-authorship networks.