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A common goal in graph visualization research is the design of novel techniques for displaying an overview of an entire graph. However, there are many situations where such an overview is not relevant or practical for users, as analyzing the global structure may not be related to the main task of the users that have semi-specific information needs. Furthermore, users accessing large graph databases through an online connection or users running on less powerful (mobile) hardware simply do not have the resources needed to compute these overviews. In this paper, we advocate an interaction model that allows users to remotely browse the immediate context graph around a specific node of interest. We show how Furnas' original degree of interest function can be adapted from trees to graphs and how we can use this metric to extract useful contextual subgraphs, control the complexity of the generated visualization and direct users to interesting datapoints in the context. We demonstrate the effectiveness of our approach with an exploration of a dense online database containing over 3 million legal citations.