In this paper, we investigate Confluent Drawings (CD), a technique for bundling edges in node-link diagrams based on network connectivity. Edge-bundling techniques are designed to reduce edge clutter in node-link diagrams by coalescing lines into common paths or bundles. Unfortunately, traditional bundling techniques introduce ambiguity since edges are only bundled by spatial proximity, rather than network connectivity; following an edge from its source to its target can lead to the perception of incorrect connectivity if edges are not clearly separated within the bundles. Contrary, CDs bundle edges based on common sources or targets. Thus, a smooth path along a confluent bundle indicates precise connectivity. While CDs have been described in theory, practical investigation and application to real-world networks (i.e., networks beyond those with certain planarity restrictions) is currently lacking. Here, we provide the first algorithm for constructing CDs from arbitrary directed and undirected networks and present a simple layout method, embedded in a sand box environment providing techniques for interactive exploration. We then investigate patterns and artifacts in CDs, which we compare to other common edge-bundling techniques. Finally, we present the first user study that compares edge-compression techniques, including CD, power graphs, metro-style, and common edge bundling. We found that users without particular expertise in visualization or network analysis are able to read small CDs without difficulty. Compared to existing bundling techniques, CDs are more likely to allow people to correctly perceive connectivity.