Participant-invariant, evolving patterns of influence in dynamic networks

Understanding the evolution of influence in dynamic networks is crucial for revealing the underlying mechanisms of complex interactions in social, biological, and information systems. Despite its importance, the temporal patterns of influence in such networks remain largely unexplored. A significant challenge in these investigations lies in the perception that networks, often consisting of thousands of nodes, entail too many evolving influence processes to be feasibly analyzed. In this study, we uncover a participant-invariant characteristic within the influence dynamics of real-world networks. Specifically, we demonstrate that a small number of influence patterns (often just one) can effectively capture the overall behavior of a network, regardless of its size. Through extensive experiments on 50 dynamic network datasets from diverse domains, we identify these patterns and quantify node participation levels via associated weights. Our findings further reveal that influence patterns within networks of the same category exhibit striking similarities, and the distribution of node weights follows a power law, indicating a high degree of heterogeneity in node participation levels. These insights streamline the representation of dynamic networks and provide a framework for understanding the evolution of influence in complex systems.