We present a hybrid visualization technique for compound graphs (i.e. networks with a hierarchical clustering defined on the nodes) that combines the use of adjacency matrices, node-link and arc diagrams to show the graph, and also combines the use of nested inclusion and icicle diagrams to show the hierarchical clustering. The graph visualized with our technique may have edges that are weighted and/or directed. We first explore the design space of visualizations of compound graphs and present a taxonomy of hybrid visualization techniques. We then present our prototype, which allows clusters (i.e. subtrees) of nodes to be grouped into matrices or split apart using a radial menu. We also demonstrate how our prototype can be used in the software engineering domain, and compare it to the commercial matrix-based visualization tool Lattix using a qualitative user study.