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We describe TopoLayout, a feature-based, multilevel algorithm that draws undirected graphs based on the topological features they contain. Topological features are detected recursively inside the graph, and their subgraphs are collapsed into single nodes, forming a graph hierarchy. Each feature is drawn with an algorithm tuned for its topology. As would be expected from a feature-based approach, the runtime and visual quality of TopoLayout depends on the number and types of topological features present in the graph. We show experimental results comparing speed and visual quality for TopoLayout against four other multilevel algorithms on a variety of data sets with a range of connectivities and sizes. TopoLayout frequently improves the results in terms of speed and visual quality on these data sets.