Spline tie-decay temporal networks
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918012701900800 |
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| author | Thongprayoon, Chanon Masuda, Naoki |
| author_facet | Thongprayoon, Chanon Masuda, Naoki |
| contents | Increasing amounts of data are available on temporal, or time-varying, networks. There have been various representations of temporal network data each of which has different advantages for downstream tasks such as mathematical analysis, visualizations, agent-based and other dynamical simulations on the temporal network, and discovery of useful structure. The tie-decay network is a representation of temporal networks whose advantages include the capability of generating continuous-time networks from discrete time-stamped contact event data with mathematical tractability and a low computational cost. However, the current framework of tie-decay networks is limited in terms of how each discrete contact event can affect the time-dependent tie strength (which we call the kernel). Here we extend the tie-decay network model in terms of the kernel. Specifically, we use a cubic spline function for modeling short-term behavior of the kernel and an exponential decay function for long-term behavior, and graft them together. This spline version of tie-decay network enables delayed and $C^1$-continuous interaction rates between two nodes while it only marginally increases the computational and memory burden relative to the conventional tie-decay network. We show mathematical properties of the spline tie-decay network and numerically showcase it with three tasks: network embedding, a deterministic opinion dynamics model, and a stochastic epidemic spreading model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spline tie-decay temporal networks Thongprayoon, Chanon Masuda, Naoki Physics and Society Increasing amounts of data are available on temporal, or time-varying, networks. There have been various representations of temporal network data each of which has different advantages for downstream tasks such as mathematical analysis, visualizations, agent-based and other dynamical simulations on the temporal network, and discovery of useful structure. The tie-decay network is a representation of temporal networks whose advantages include the capability of generating continuous-time networks from discrete time-stamped contact event data with mathematical tractability and a low computational cost. However, the current framework of tie-decay networks is limited in terms of how each discrete contact event can affect the time-dependent tie strength (which we call the kernel). Here we extend the tie-decay network model in terms of the kernel. Specifically, we use a cubic spline function for modeling short-term behavior of the kernel and an exponential decay function for long-term behavior, and graft them together. This spline version of tie-decay network enables delayed and $C^1$-continuous interaction rates between two nodes while it only marginally increases the computational and memory burden relative to the conventional tie-decay network. We show mathematical properties of the spline tie-decay network and numerically showcase it with three tasks: network embedding, a deterministic opinion dynamics model, and a stochastic epidemic spreading model. |
| title | Spline tie-decay temporal networks |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2408.11913 |