Matrix-weighted networks for modeling multidimensional dynamics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912062165221376 |
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| author | Tian, Yu Kojaku, Sadamori Sayama, Hiroki Lambiotte, Renaud |
| author_facet | Tian, Yu Kojaku, Sadamori Sayama, Hiroki Lambiotte, Renaud |
| contents | Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often have multiple interconnected opinions that can affect different opinions of other individuals, which can be better characterized by matrices. We propose a novel, general framework for modeling such multidimensional interacting dynamics: matrix-weighted networks (MWNs). We present the mathematical foundations of MWNs and examine consensus dynamics and random walks within this context. Our results reveal that the coherence of MWNs gives rise to non-trivial steady states that generalize the notions of communities and structural balance in traditional networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix-weighted networks for modeling multidimensional dynamics Tian, Yu Kojaku, Sadamori Sayama, Hiroki Lambiotte, Renaud Social and Information Networks Machine Learning Mathematical Physics Physics and Society 05C22, 05C50, 05C81, 37E25, 39A06, 91D30, 94C15 Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often have multiple interconnected opinions that can affect different opinions of other individuals, which can be better characterized by matrices. We propose a novel, general framework for modeling such multidimensional interacting dynamics: matrix-weighted networks (MWNs). We present the mathematical foundations of MWNs and examine consensus dynamics and random walks within this context. Our results reveal that the coherence of MWNs gives rise to non-trivial steady states that generalize the notions of communities and structural balance in traditional networks. |
| title | Matrix-weighted networks for modeling multidimensional dynamics |
| topic | Social and Information Networks Machine Learning Mathematical Physics Physics and Society 05C22, 05C50, 05C81, 37E25, 39A06, 91D30, 94C15 |
| url | https://arxiv.org/abs/2410.05188 |