A Shape Change Enhancing Hierarchical Layout for the Pairwise Comparison of Directed Acyclic Graphs

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\%.