U-centrality: A Network Centrality Measure Based on Minimum Energy Control for Laplacian Dynamics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918394763149312 |
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| author | Zheng, Xinran Massai, Leonardo Franceschetti, Massimo Touri, Behrouz |
| author_facet | Zheng, Xinran Massai, Leonardo Franceschetti, Massimo Touri, Behrouz |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_00339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | U-centrality: A Network Centrality Measure Based on Minimum Energy Control for Laplacian Dynamics Zheng, Xinran Massai, Leonardo Franceschetti, Massimo Touri, Behrouz Social and Information Networks Optimization and Control 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. |
| title | U-centrality: A Network Centrality Measure Based on Minimum Energy Control for Laplacian Dynamics |
| topic | Social and Information Networks Optimization and Control |
| url | https://arxiv.org/abs/2511.00339 |