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

翻译：摘要：本文提出VMap，一种类地图的矩形空间填充可视化方法，用于实现顶点中心的图探索。现有可视化方法在矩形宽高比、顶点-边交叉以及数据编码精度等质量优化方面存在局限性。为解决此问题，VMap整合了三个创新组件：(1) 期望宽高比(DAR)矩形分割算法，(2) 两阶段矩形调整算法，以及(3) 基于模拟退火的启发式优化器。首先，为生成输入图的矩形空间填充布局，我们将图的二维嵌入细分为矩形，并优化矩形的宽高比以趋近期望值。其次，为在矩形间路由图边且避免顶点-边遮挡，我们设计了两阶段算法调整矩形布局，在矩形间插入边界空间。第三，为综合考虑多种视觉标准生成并排列矩形，我们设计了基于模拟退火的启发式优化方法，通过调整顶点二维嵌入来权衡宽高比质量与顶点权重及邻接关系的编码精度。我们在合成数据集与应用数据集上评估了VMap的有效性。在二维点的矩形分割任务中，与现有方法相比，VMap生成的矩形布局在合成数据上具有更优的宽高比质量。在三个真实世界数据集上，VMap在图的矩形布局生成中实现了更高的编码精度与更快的生成速度。通过社交网络可视化、学术社区表征及地理信息展示三个案例研究，我们进一步论证了VMap在顶点中心图探索中的实用性。