{"ID":2847140,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00339","arxiv_id":"2511.00339","title":"U-centrality: A Network Centrality Measure Based on Minimum Energy Control for Laplacian Dynamics","abstract":"Network centrality is a foundational concept for quantifying the importance of nodes within a network. Many traditional centrality measures--such as degree and betweenness centrality--are purely structural and often overlook the dynamics that unfold across the network. However, the notion of a node's importance is inherently context-dependent and must reflect both the system's dynamics and the specific objectives guiding its operation. Motivated by this perspective, we propose a dynamic, task-aware centrality framework rooted in optimal control theory. By formulating a problem on minimum energy control of average opinion based on Laplacian dynamics and focusing on the variance of terminal state, we introduce a novel centrality measure--termed U-centrality--that quantifies a node's ability to unify the agents' state. We demonstrate that U-centrality interpolates between known measures: it aligns with degree centrality in the short-time horizon and converges to a new centrality over longer time scales which is closely related to current-flow closeness centrality. This work bridges structural and dynamical approaches to centrality, offering a principled, versatile tool for network analysis in dynamic environments.","short_abstract":"Network centrality is a foundational concept for quantifying the importance of nodes within a network. Many traditional centrality measures--such as degree and betweenness centrality--are purely structural and often overlook the dynamics that unfold across the network. However, the notion of a node's importance is inhe...","url_abs":"https://arxiv.org/abs/2511.00339","url_pdf":"https://arxiv.org/pdf/2511.00339v2","authors":"[\"Xinran Zheng\",\"Leonardo Massai\",\"Massimo Franceschetti\",\"Behrouz Touri\"]","published":"2025-11-01T00:49:56Z","proceeding":"cs.SI","tasks":"[\"cs.SI\",\"math.OC\"]","methods":"[]","has_code":false}