Opinion dynamics on directed complex networks
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929204941029376 |
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| author | Fraiman, Nicolas Lin, Tzu-Chi Olvera-Cravioto, Mariana |
| author_facet | Fraiman, Nicolas Lin, Tzu-Chi Olvera-Cravioto, Mariana |
| contents | We propose and analyze a mathematical model for the evolution of opinions on directed complex networks. Our model generalizes the popular DeGroot and Friedkin-Johnsen models by allowing vertices to have attributes that may influence the opinion dynamics. We start by establishing sufficient conditions for the existence of a stationary opinion distribution on any fixed graph, and then provide an increasingly detailed characterization of its behavior by considering a sequence of directed random graphs having a local weak limit. Our most explicit results are obtained for graph sequences whose local weak limit is a marked Galton-Watson tree, in which case our model can be used to explain a variety of phenomena, e.g., conditions under which consensus can be achieved, mechanisms in which opinions can become polarized, and the effect of disruptive stubborn agents on the formation of opinions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2209_00969 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Opinion dynamics on directed complex networks Fraiman, Nicolas Lin, Tzu-Chi Olvera-Cravioto, Mariana Probability Social and Information Networks Physics and Society 60G10, 05C80, 60J05, 60J85 We propose and analyze a mathematical model for the evolution of opinions on directed complex networks. Our model generalizes the popular DeGroot and Friedkin-Johnsen models by allowing vertices to have attributes that may influence the opinion dynamics. We start by establishing sufficient conditions for the existence of a stationary opinion distribution on any fixed graph, and then provide an increasingly detailed characterization of its behavior by considering a sequence of directed random graphs having a local weak limit. Our most explicit results are obtained for graph sequences whose local weak limit is a marked Galton-Watson tree, in which case our model can be used to explain a variety of phenomena, e.g., conditions under which consensus can be achieved, mechanisms in which opinions can become polarized, and the effect of disruptive stubborn agents on the formation of opinions. |
| title | Opinion dynamics on directed complex networks |
| topic | Probability Social and Information Networks Physics and Society 60G10, 05C80, 60J05, 60J85 |
| url | https://arxiv.org/abs/2209.00969 |