Graph visualization has been successfully applied in a wide range of problems and applications. Although different approaches are available to create visual representations, most of them suffer from clutter when faced with many nodes and/or edges. Among the techniques that address this problem, edge bundling has attained relative success in improving node-link layouts by bending and aggregating edges. Despite their success, most approaches perform the bundling based only on visual space information. There is no explicit connection between the produced bundled visual representation and the underlying data (edges or vertices attributes). In this paper, we present a novel edge bundling technique, called Similarity-Driven Edge Bundling (SDEB), to address this issue. Our method creates a similarity hierarchy based on a multilevel partition of the data, grouping edges considering the similarity between nodes to guide the bundling. The novel features introduced by SDEB are explored in different application scenarios, from dynamic graph visualization to multilevel exploration. Our results attest that SDEB produces layouts that consistently follow the similarity relationships found in the graph data, resulting in semantically richer presentations that are less cluttered than the state-of-the-art.