From Signed Networks to Group Graphs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909692335226880 |
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| author | Evans, Tim S. |
| author_facet | Evans, Tim S. |
| contents | I define a "group graph" which encodes the symmetry in a dynamical process on a network. Group graphs extend signed networks, where links are labelled with plus or minus one, by allowing link labels from any group and generalising the standard notion of balance. I show that for processes on a balanced group graph the time evolution is completely determined by the network topology, not by the group structure. This unifies and extends recent findings on signed networks (Tian \& Lambiotte, 2024a) and complex networks (Tian \& Lambiotte, 2024b). I will also relate the results discussed here to related work such as the "group graph" of Harary (1982), a "voltage graph" (Gross, 1974) and a "gain graph" (Zaslavsky 1989). Finally, I will review some promising applications for network dynamics and symmetry-driven modelling including status, edges with a zero label, weak balance, unbalanced group graphs and using monoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Signed Networks to Group Graphs Evans, Tim S. Physics and Society Discrete Mathematics Social and Information Networks I define a "group graph" which encodes the symmetry in a dynamical process on a network. Group graphs extend signed networks, where links are labelled with plus or minus one, by allowing link labels from any group and generalising the standard notion of balance. I show that for processes on a balanced group graph the time evolution is completely determined by the network topology, not by the group structure. This unifies and extends recent findings on signed networks (Tian \& Lambiotte, 2024a) and complex networks (Tian \& Lambiotte, 2024b). I will also relate the results discussed here to related work such as the "group graph" of Harary (1982), a "voltage graph" (Gross, 1974) and a "gain graph" (Zaslavsky 1989). Finally, I will review some promising applications for network dynamics and symmetry-driven modelling including status, edges with a zero label, weak balance, unbalanced group graphs and using monoids. |
| title | From Signed Networks to Group Graphs |
| topic | Physics and Society Discrete Mathematics Social and Information Networks |
| url | https://arxiv.org/abs/2505.22802 |