Graph drawing readability metrics are routinely used to assess and create node-link layouts of network data. Existing readability metrics fall short in three ways. The many count-based metrics such as edge-edge or node-edge crossings simply provide integer counts, missing the opportunity to quantify the amount of overlap between items, which may vary in size, at a more fine-grained level. Current metrics focus solely on single-level topological structure, ignoring the possibility of multi-level structure such as large and thus highly salient metanodes. Most current metrics focus on the measurement of clutter in the form of crossings and overlaps, and do not take into account the trade-off between the clutter and the information sparsity of the drawing, which we refer to as sprawl. We propose an area-aware approach to clutter metrics that tracks the extent of geometric overlaps between node-node, node-edge, and edge-edge pairs in detail. It handles variable-size nodes and explicitly treats metanodes and leaf nodes uniformly. We call the combination of a sprawl metric and an area-aware clutter metric a sprawlter metric. We present an instantiation of the sprawlter metrics featuring a formal and thorough discussion of the crucial component, the penalty mapping function. We implement and validate our proposed metrics with extensive computational analysis of graph layouts, considering four layout algorithms and 56 layouts encompassing both real-world data and synthetic examples illustrating specific configurations of interest.

中文翻译：

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蔓延图可读性指标：结合蔓延和区域感知混乱


图形绘制可读性度量通常用于评估和创建网络数据的节点链接布局。现有的可读性指标在三个方面存在不足。许多基于计数的度量（例如边缘-边缘或节点-边缘交叉）仅提供整数计数，错过了在更细粒度的级别上量化项目之间重叠量的机会，这些重叠量的大小可能会有所不同。当前的指标仅关注单层拓扑结构，忽略了多层结构的可能性，例如大型且高度显着的元节点。当前大多数指标都侧重于以交叉和重叠的形式测量杂乱，而没有考虑杂乱与绘图信息稀疏性之间的权衡，我们将其称为蔓延。我们提出了一种区域感知的杂波度量方法，该方法详细跟踪节点-节点、节点-边缘和边缘-边缘对之间的几何重叠程度。它处理可变大小的节点，并显式地统一处理元节点和叶节点。我们将蔓延度量和区域感知杂乱度量的组合称为蔓延度量。我们提出了蔓延指标的实例，其中对关键组成部分（惩罚映射函数）进行了正式和彻底的讨论。我们通过对图形布局的广泛计算分析来实现和验证我们提出的指标，考虑四种布局算法和 56 个布局，其中包含真实世界数据和说明感兴趣的特定配置的合成示例。