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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21721 |
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| _version_ | 1866912789288714240 |
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| author | Li, Hsin-Lun |
| author_facet | Li, Hsin-Lun |
| contents | We study a discrete-time consensus model in which agents iteratively update their states through interactions on a dynamic social network. At each step, a single agent is selected asynchronously and averages the values of its current neighbors. A distinctive feature of our model is that an agent's neighborhood may contract following an update, while non-selected agents may add or remove neighbors independently. This creates a time-varying communication structure with endogenous contraction. We show that under mild assumptions--specifically, that the evolving graph is connected infinitely often--the system reaches consensus almost surely. Our results extend classical consensus theory on time-varying graphs and asynchronous updates by introducing selective neighborhood contraction, offering new insights into agreement dynamics in evolving social systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asynchronous Averaging on Dynamic Graphs with Selective Neighborhood Contraction Li, Hsin-Lun Systems and Control Mathematical Physics Dynamical Systems Primary 93D50, 93D20, Secondary 93C10, 05C82, 60G42 We study a discrete-time consensus model in which agents iteratively update their states through interactions on a dynamic social network. At each step, a single agent is selected asynchronously and averages the values of its current neighbors. A distinctive feature of our model is that an agent's neighborhood may contract following an update, while non-selected agents may add or remove neighbors independently. This creates a time-varying communication structure with endogenous contraction. We show that under mild assumptions--specifically, that the evolving graph is connected infinitely often--the system reaches consensus almost surely. Our results extend classical consensus theory on time-varying graphs and asynchronous updates by introducing selective neighborhood contraction, offering new insights into agreement dynamics in evolving social systems. |
| title | Asynchronous Averaging on Dynamic Graphs with Selective Neighborhood Contraction |
| topic | Systems and Control Mathematical Physics Dynamical Systems Primary 93D50, 93D20, Secondary 93C10, 05C82, 60G42 |
| url | https://arxiv.org/abs/2512.21721 |