Social networks collected by historians or sociologists typically have a large number of actors and edge attributes. Applying social network analysis (SNA) algorithms to these networks produces additional attributes such as degree, centrality, and clustering coefficients. Understanding the effects of this plethora of attributes is one of the main challenges of multivariate SNA. We present the design of GraphDice, a multivariate network visualization system for exploring the attribute space of edges and actors. GraphDice builds upon the ScatterDice system for its main multidimensional navigation paradigm, and extends it with novel mechanisms to support network exploration in general and SNA tasks in particular. Novel mechanisms include visualization of attributes of interval type and projection of numerical edge attributes to node attributes. We show how these extensions to the original ScatterDice system allow to support complex visual analysis tasks on networks with hundreds of actors and up to 30 attributes, while providing a simple and consistent interface for interacting with network data.