Online dynamic network visualization is imperative for real-time network monitoring and analysis applications. It presents a significant research challenge for maintaining both layout stability and quality amid unpredictable temporal changes. While node-link diagrams are extensively utilized in online dynamic network visualization, previous node-link-diagram-based research primarily focused on stabilizing the layout by defining constraints on local node movement. However, these constraints often neglect the structural influence and its corresponding global impact, which may lead to that the representations of the network structure change significantly over time and a decrease in layout quality. To address this problem, we introduce the Structure-based Influence Propagation and Aging (SIPA) algorithm, a novel approach to preserve the stability of relative node positions and shapes of interconnected nodes (referred to as structures) between adjacent time steps. These stable structures serve as visual cues for users tracking the evolution of the network, thereby enhancing the overall layout stability. Additionally, we enhance dynamic network analysis by a highly interactive visualization system, enriching the layout result with multiple coordinated views of temporal trends, network features, animated graph diaries and snapshots. Our approach empowers users to interactively track and compare network evolution within a long-term temporal context and across multiple aspects. We demonstrate the effectiveness and performance of our approach through in-lab user studies and comparative experiments with three baseline dynamic network layout methods.