Opinion dynamics on signed graphs and graphons: Beyond the piece-wise constant case (Extended version)
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916378505641984 |
|---|---|
| author | Prisant, Raoul Garin, Federica Frasca, Paolo |
| author_facet | Prisant, Raoul Garin, Federica Frasca, Paolo |
| contents | In this paper we make use of graphon theory to study opinion dynamics on large undirected networks. The opinion dynamics models that we take into consideration allow for negative interactions between the individuals, i.e. competing entities whose opinions can grow apart. We consider both the repelling model and the opposing model that are studied in the literature. We define the repelling and the opposing dynamics on graphons and we show that their initial value problem's solutions exist and are unique. We then show that the graphon dynamics well approximate the dynamics on large graphs that converge to a graphon. This result applies to large random graphs that are sampled according to a graphon. All these facts are illustrated in an extended numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Opinion dynamics on signed graphs and graphons: Beyond the piece-wise constant case (Extended version) Prisant, Raoul Garin, Federica Frasca, Paolo Physics and Society Systems and Control In this paper we make use of graphon theory to study opinion dynamics on large undirected networks. The opinion dynamics models that we take into consideration allow for negative interactions between the individuals, i.e. competing entities whose opinions can grow apart. We consider both the repelling model and the opposing model that are studied in the literature. We define the repelling and the opposing dynamics on graphons and we show that their initial value problem's solutions exist and are unique. We then show that the graphon dynamics well approximate the dynamics on large graphs that converge to a graphon. This result applies to large random graphs that are sampled according to a graphon. All these facts are illustrated in an extended numerical example. |
| title | Opinion dynamics on signed graphs and graphons: Beyond the piece-wise constant case (Extended version) |
| topic | Physics and Society Systems and Control |
| url | https://arxiv.org/abs/2404.08372 |