Noções de grafos dirigidos, cadeias de Markov e as buscas do Google

• Ano de defesa: 2014
• Autor(a) principal: Oliveira, José Carlos Francisco de
• Orientador(a): Cardoso, José Anderson Valença
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Sergipe
• Programa de Pós-Graduação: Mestrado Profissional em Matemática
• País: Brasil
• Palavras-chave em Português: Matemática; Processos de Markov; Matrizes (Matemática); Sistemas lineares; Probabilidades; Sites da Web; Google; Ferramentas de busca na Web; Grafos dirigidos; Passeios aleatórios; Cadeias de Markov; PageRank; Vetor estado estacionário; Buscador Google
• Palavras-chave em Inglês: Matrices; Linear systems; Probability; Directed graphs; Random walks; Markov chains; Steady state vector; Google search engine
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://ri.ufs.br/handle/riufs/6482

This paper has as its main purpose to highlight some mathematical concepts, which are behind the ranking given by a research made on the website mostly used in the world: Google. At the beginning, we briefly approached some High School’s concepts, such as: Matrices, Linear Systems and Probability. After that, we presented some basic notions related to Directed Graphs and Markov Chains of Discrete Time. From this last one, we gave more emphasis to the Steady State Vector because it ensures foreknowledge results from long-term. These concepts are extremely important to our paper, because they will be used to explain the involvement of Mathematic behind the web search “Google”. Then, we tried to detail the ranking operation of the search pages on Google, i.e., how the results of a research are classified, determining which results are presented in a sequential way in order of relevance. Finally we obtained “PageRank”, an algorithm which creates what we call Google’s Matrices and ranks the pages of a search. We finished making a brief comment about the historical arising of the web searches, from their founders to the rise and hegemony of Google.