Conectividade do grafo aleatório de Erdös-Rényi e uma variante com conexões locais

• Autor(a) principal: Bedia, Elizbeth Chipa
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/7493
• topic: Conectividade; Grafos aleatórios; Transição de fase; Probabilidade; Connectivity; Random graphs; Phase transition; Probability; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::FUNDAMENTOS DA ESTATISTICA

We say that a graph is connected if there is a path edges between any pair of vertices. Random graph Erd os-R enyi with n vertices is obtained by connecting each pair of vertex with probability pn 2 (0; 1) independently of the others. In this work, we studied in detail the connectivity threshold in the connection probability pn for random graphs Erd os-R enyi when the number of vertices n diverges. For this study, we review some basic probabilistic tools (convergence of random variables and methods of the rst and second moment), which will lead to a better understanding of more complex results. In addition, we apply the above concepts for a model with a simple topology, speci cally studied the asymptotic behavior of the probability of non-existence of isolated vertices, and we discussed the connectivity or not of the graph. Finally we show the convergence in distribution of the number of isolated vertices for a Poisson distribution of the studied model.