In various embodiments, a visualization engine generates graphs that facilitate sense making operations on data sets. A graph includes nodes that are associated with a data set and edges that represent relationships between the nodes. In operation, the visualization engine computes pairwise similarities between the nodes. Subsequently, the visualization engine computes a layout for the graph based on the pairwise similarities and user-specified constraints. Finally, the visualization engine renders a graph for display based on the layout, the nodes, and the edges. Advantageously, by interactively specifying constraints and then inspecting the topology of the automatically generated graph, the user may efficiently explore salient aspects of the data set.