## 2 Related Work
### Dynamic Graph Layout Methods  
Many algorithms have been proposed on dynamic network layout. These algorithms aim to preserve user's mental maps [11; 18; 19] as network structures change over time, ensuring a coherent layout sequence that aids users in understanding the network evolution, yet the layout quality must adhere to aesthetic criteria [10; 20]. Based on data requirement, dynamic network layout methods can be classified into two categories: offline methods and online methods.  
Offline method:Offline methods, where all network states of the entire time spans are known, can pre-adjust node positions to accommodate forthcoming nodes, and minimize layout changes to better maintain the user's mental map, often employing the concept of \"hypergraphs [12]\" for layout. However, such offline methods have higher demand on data, all network states to be visualized need to be known in advance, and does not suit to the real-time dynamic network layout scenarios.  
**Online method:** Many real-world networks are also likely to be streaming over time. A streaming graph is a continuous, unbounded, rapid, time-varying stream of edges that is clearly too large to fit in memory except for probably short windows of time [21]. For monitoring the streaming networks in real time, online dynamic layout methods are required. Online layout methods face greater challenges considering the upcoming changes are unpredictable. Their goal is to minimize visual changes between the original and modified layouts when new network update comes, enabling users to swiftly comprehend graphical changes. [PERSON] [19] was among the pioneers in online layout algorithms, developing techniques that conserve mental maps while generating aesthetically pleasing layouts. Common practice in online network drawing involves adding constraints to nodes, limiting their mobility and ensuring a consistent mental map across the sequence of graphs [22]. Pinning algorithms [22] employ simulated annealing to reduce node displacement between adjacent layouts. The Aging algorithm [16] introduces node and edge age, calculated based on node appearance time and lifetime exposure to motion, yielding relatively stable positions for long-term stable nodes. [PERSON] et al. [17] extended FM3 to accommodate dynamic network data, proposing a refinement scheme grounded in node energy to allow highly influential nodes to adjust their positions within the layout. [PERSON] et al. [23] introduced the DIG-COLA algorithm, building on the KK algorithm and incorporating directional constraints for drawing directed networks. [PERSON] et al. [24] and [PERSON] [25] introduced multiple constraints, encompassing circular, distance, and directional constraints, even enabling users to define structures to generate network layouts. LCDE [26] employs a distance-constrained stress model in online dynamic network drawing. These methods primarily handle the local changes, while neglect the influence to the global structure and shapes.  
In this paper, we contribute to the online dynamic node-link diagram layout field by introducing the Structure-based Influence Propagation and Aging (SIPA) layout algorithm. The SIPA is tailored to address the challenges of balancing the network stability and overall network layout quality.