Comparing directed acyclic graphs is essential in various fields such as healthcare, social media, finance, biology, and marketing. DAGs often result from contagion processes over networks, including information spreading, retweet activity, disease transmission, financial crisis propagation, malware spread, and gene mutations. For instance, in disease spreading, an infected patient can transmit the disease to contacts, making it crucial to analyze and predict scenarios. Similarly, in finance, understanding the effects of saving or not saving specific banks during a crisis is vital. Experts often need to identify small differences between DAGs, such as changes in a few nodes or edges. Even the presence or absence of a single edge can be significant. Visualization plays a crucial role in facilitating these comparisons. However, standard hierarchical layout algorithms struggle to visualize subtle changes effectively. The typical hierarchical layout, with the root on top, is preferred due to its performance in comparison to other layouts. Nevertheless, these standard algorithms prioritize single-graph aesthetics over comparison suitability, making it challenging for users to spot changes. To address this issue, we propose a layout that enhances shape changes in DAGs while minimizing the impact on aesthetics. Our approach involves outwardly swapping changes, altering the DAG's shape. We introduce new drawing criteria. Our layout builds upon a Sugiyama-like hierarchical layout and implements these criteria through two extensions. We designed it this way to maintain interchangeability and accommodate future optimizations, such as pseudo-nodes for edge crossing minimization. In our evaluations, our layout achieves excellent results, with edge crossing aesthetics averaging around 0.8 (on a scale of 0 to 1). Additionally, our layout outperforms the base implementation by an average of 60-75\%.

翻译：有向无环图（DAG）的比较在医疗健康、社交媒体、金融、生物学和市场营销等多个领域至关重要。DAG通常源于网络上的传播过程，包括信息扩散、转发活动、疾病传播、金融危机蔓延、恶意软件传播和基因突变。例如，在疾病传播中，受感染的患者可能将疾病传染给接触者，因此分析和预测传播场景至关重要。同样，在金融领域，理解危机期间救助或不救助特定银行的影响也极为重要。专家通常需要识别DAG之间的细微差异，例如少数节点或边的变化。即使单条边的存在与否也可能具有重大意义。可视化在促进此类比较中发挥着关键作用。然而，标准的层次布局算法难以有效呈现细微变化。典型的层次布局（根节点位于顶部）因其相较于其他布局的性能优势而备受青睐。尽管如此，这些标准算法优先考虑单图的美学效果而非比较适用性，导致用户难以发现变化。为解决此问题，我们提出一种布局方法，既能增强DAG的形状变化，又能最小化对美学效果的影响。我们的方法通过向外交换变化来改变DAG的形状。我们引入了新的绘制标准。该布局基于类Sugiyama层次布局，并通过两个扩展实现这些标准。如此设计旨在保持可互换性并适应未来优化，例如用于边交叉最小化的伪节点。在评估中，我们的布局取得了优异效果，边交叉美学指标平均约为0.8（量程为0至1）。此外，我们的布局性能平均比基础实现高出60-75%。