## 1 Introduction  
A network is the combination of a set of entities and the relationships between them [1]. Network visualization provides a visual means for analyzing the relation data and finds wide-ranging applications across multiple domains [2], spanning from transportation systems [3], social networks [4], biological networks [5, 6], contact tracings [7], to academic writing analysis [8]. By nature, a significant portion of these networks is dynamic, where nodes and edges evolve over time. The challenge in visualizing dynamic networks is to compute a new layout that are both aesthetically pleasing and fits well into the sequence of drawings of the evolving graph [9]. The former criterion is about layout quality [10], and the latter criterion is about maintaining the layout stability, also termed as the mental map [11]. Many dynamic layout methods have been developed to address these challenges. The offline methods, where the entire sequence of the graphs to be drawn is known, can pre-adjust node positions to accommodate forthcoming graph changes [12, 13] and produce relatively stable layouts across the entire time spans. In contrast, for real-time network monitoring and analysis applications, online layout methods are required. Sincethe upcoming changes are unknown, online layout methods are more challenging in terms of stability maintenance [9; 14]. Node-link diagrams are extremely common and is a widely employed network layout technique [15]. Existing node-link-diagram-based online layout algorithms [9; 16; 17] primarily address this challenge by restricting the movements of local nodes while overlook broader influences, potentially resulting in failures to adequately represent the stable structures or the overall shape of the network. In this context, the network structures refer to the shape and relative positions for interconnected nodes. Stable structures persisting across consecutive time steps serve as anchors, facilitating users in tracing the network evolution, and therefore are important for ensuring the overall layout stability. Consequently, the development of new techniques becomes imperative to augment the handling of this issue. On the one hand, enhancing layout techniques is essential. On the other hand, it is challenging for human users to fully comprehend the network evolution by solely viewing the layout result. Visualization systems with multiple auxiliary views and rich interactions can effectively enhance user perception. To address these challenges, we introduce a novel Structure-based Influence Propagation and Aging (SIPA) dynamic node-link diagram layout algorithm, and augmente the layout result with the design of an interactive visualization system. This not only enhances users' understanding of evolving network structures, but also facilitates the exploration and comparison of network dynamics. Our main contributions in this research can be summarized as follows:  
1. We extend previous online dynamic layout methods by a novel SIPA layout algorithm. This algorithm is proposed based on the influence of structural changes to different nodes, and with a combination of node ages. While ensuring layout quality, our algorithm better preserves the relative positions and shapes of structures that persist across adjacent time steps. These stable structures provide anchors for tracing the network evolution and thus contributes to enhancing the overall layout stability. 2. We design and implement an interactive visualization system that enriches dynamic network analysis with multiple coordinated views. The system provides crucial temporal aspects and features of dynamic networks, enhancing exploration, tracking, and comparison of network dynamics. 3. We verify the performance of our algorithm by comparative experiments based on three dynamic network datasets; and we demonstrate the usability and effectiveness of our system through use cases and a user study. The following sections of this paper is organized as follows: we first review the related work in Section 2.