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Graph visualization has been widely used to understand and present both global structural and local adjacency information in relational data sets (e.g., transportation networks, citation networks, or social networks). Graphs with dense edges, however, are difficult to visualize because fast layout and good clarity are not always easily achieved. When the number of edges is large, edge bundling can be used to improve the clarity, but in many cases, the edges could be still too cluttered to permit correct interpretation of the relations between nodes. In this paper, we present an ambiguity-free edge-bundling method especially for improving local detailed view of a complex graph. Our method makes more efficient use of display space and supports detail-on-demand viewing through an interactive interface. We demonstrate the effectiveness of our method with public coauthorship network data.