When exploiting the power of node-link diagrams to represent real-world data such as web structures, airline routes, electrical, telecommunication and social networks, link congestion frequently arises. Such areas in the diagram—with dense, overlapping links—are not readable: connectivity, node shapes, labels, and contextual information are obscured. In response, graph-layout research has begun to consider the modification of link shapes with techniques such as link routing and bundling. In this paper, we delve into the interactive techniques afforded by variant use of link curvature, delineating a six-dimensional design space that is populated by four families of interactive techniques: bundling, fanning, magnets, and legends. Our taxonomy encompasses existing techniques and reveals several novel link interactions. We describe the implementation of these techniques and illustrate their potential for exploring dense graphs with multiple types of links.