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We present VMap, a map-like rectangular space-filling visualization, toperform vertex-centric graph exploration. Existing visualizations have limitedsupport for quality optimization among rectangular aspect ratios, vertex-edgeintersection, and data encoding accuracy. To tackle this problem, VMapintegrates three novel components: (1) a desired-aspect-ratio (DAR) rectangularpartitioning algorithm, (2) a two-stage rectangle adjustment algorithm, and (3)a simulated annealing based heuristic optimizer. First, to generate arectangular space-filling layout of an input graph, we subdivide the 2Dembedding of the graph into rectangles with optimization of rectangles' aspectratios toward a desired aspect ratio. Second, to route graph edges betweenrectangles without vertex-edge occlusion, we devise a two-stage algorithm toadjust a rectangular layout to insert border space between rectangles. Third,to produce and arrange rectangles by considering multiple visual criteria, wedesign a simulated annealing based heuristic optimization to adjust vertices'2D embedding to support trade-offs among aspect ratio quality and the encodingaccuracy of vertices' weights and adjacency. We evaluated the effectiveness ofVMap on both synthetic and application datasets. The resulting rectangularlayout has better aspect ratio quality on synthetic data compared with theexisting method for the rectangular partitioning of 2D points. On threereal-world datasets, VMap achieved better encoding accuracy and attained fastergeneration speed compared with existing methods on graphs' rectangular layoutgeneration. We further illustrate the usefulness of VMap for vertex-centricgraph exploration through three case studies on visualizing social networks,representing academic communities, and displaying geographic information.

VMap: An Interactive Rectangular Space-filling Visualization for Map-like Vertex-centric Graph Exploration