Topological study of the convergence in the voter model
Abstract The voter model has been widely studied due to its simple formulation and attainable theoretical treatment. The study of the “active links”, edges that connect nodes in different states, has been a key element in the analysis of the convergence of the model. Typically, the density of active...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-12-01
|
| Series: | Applied Network Science |
| Online Access: | https://doi.org/10.1007/s41109-019-0236-y |
| _version_ | 1819072950265970688 |
|---|---|
| author | Inés Caridi Sergio Manterola Viktoriya Semeshenko Pablo Balenzuela |
| author_facet | Inés Caridi Sergio Manterola Viktoriya Semeshenko Pablo Balenzuela |
| author_sort | Inés Caridi |
| collection | DOAJ |
| description | Abstract The voter model has been widely studied due to its simple formulation and attainable theoretical treatment. The study of the “active links”, edges that connect nodes in different states, has been a key element in the analysis of the convergence of the model. Typically, the density of active links, ρ, is used to characterize the system when approaching to absorbing state. However, more information can be extracted from how the active links are distributed across the underlying network.In this paper we study the dynamics of active links in the voter model, from a perspective of complex networks. This approach allows us to understand how the dynamics of the model is mapped in topological features of a dynamical network of active links. We found that certain topological properties of the Active Link Network show salient features related to the dynamics of the model. The Active Link Network goes from a state similar to the underlying random network in the initial state to extremely disassortative graph when the dynamics approaches to absorbing state. In this state, the active link network is dominated by “star-like” motifs, where different opinions take different topological roles on the network. Thus, the Active Link Network shows some properties which are distant from the hypothesis made by the current theoretical models, which assume there are no correlations among active links. |
| first_indexed | 2024-12-21T17:45:52Z |
| format | Article |
| id | doaj.art-61a599989be14662a9e896636387e609 |
| institution | Directory Open Access Journal |
| issn | 2364-8228 |
| language | English |
| last_indexed | 2024-12-21T17:45:52Z |
| publishDate | 2019-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Applied Network Science |
| spelling | doaj.art-61a599989be14662a9e896636387e6092022-12-21T18:55:30ZengSpringerOpenApplied Network Science2364-82282019-12-014111310.1007/s41109-019-0236-yTopological study of the convergence in the voter modelInés Caridi0Sergio Manterola1Viktoriya Semeshenko2Pablo Balenzuela3Calculus Institute, University of Buenos Aires and CONICETDepartamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos AiresUniversidad de Buenos Aires. Facultad de Ciencias EconómicasDepartamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos AiresAbstract The voter model has been widely studied due to its simple formulation and attainable theoretical treatment. The study of the “active links”, edges that connect nodes in different states, has been a key element in the analysis of the convergence of the model. Typically, the density of active links, ρ, is used to characterize the system when approaching to absorbing state. However, more information can be extracted from how the active links are distributed across the underlying network.In this paper we study the dynamics of active links in the voter model, from a perspective of complex networks. This approach allows us to understand how the dynamics of the model is mapped in topological features of a dynamical network of active links. We found that certain topological properties of the Active Link Network show salient features related to the dynamics of the model. The Active Link Network goes from a state similar to the underlying random network in the initial state to extremely disassortative graph when the dynamics approaches to absorbing state. In this state, the active link network is dominated by “star-like” motifs, where different opinions take different topological roles on the network. Thus, the Active Link Network shows some properties which are distant from the hypothesis made by the current theoretical models, which assume there are no correlations among active links.https://doi.org/10.1007/s41109-019-0236-y |
| spellingShingle | Inés Caridi Sergio Manterola Viktoriya Semeshenko Pablo Balenzuela Topological study of the convergence in the voter model Applied Network Science |
| title | Topological study of the convergence in the voter model |
| title_full | Topological study of the convergence in the voter model |
| title_fullStr | Topological study of the convergence in the voter model |
| title_full_unstemmed | Topological study of the convergence in the voter model |
| title_short | Topological study of the convergence in the voter model |
| title_sort | topological study of the convergence in the voter model |
| url | https://doi.org/10.1007/s41109-019-0236-y |
| work_keys_str_mv | AT inescaridi topologicalstudyoftheconvergenceinthevotermodel AT sergiomanterola topologicalstudyoftheconvergenceinthevotermodel AT viktoriyasemeshenko topologicalstudyoftheconvergenceinthevotermodel AT pablobalenzuela topologicalstudyoftheconvergenceinthevotermodel |