Navegação em redes espacialmente correlacionadas

• Autor(a) principal: Reis, Saulo Davi Soares e
• Data de Publicação: 2009
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/12888
• topic: Física estatística; Sistemas complexos; Redes complexas; Statistical Physics; Complex systems; Complex networks

A significant number of real networks have well-defined spatial characteristics. We studied how network with spatially correlated topolgies can influence the processes of navigation through them. For this, we study the behavior of the average shortest-path length to networks defined within Kleinberg’s model [1, 2] to analyze the navigation dictated by rules of global knowledge. The Kleinberg’s model is characterized by allowing long-range connections between two vertices u and v distributed by a power-law probability distribution. For a better understanding of the topological characteristics presented by this family of networks, we applied the epidemic model susceptible-infected-susceptible (SIS) and we found that, we see that the Kleinberg’s model presents the small-world phenomenon only for a certain range of values of the clustering exponent α. We introduced a model of spatially embedded networks, conceptually based on the Kleinberg’s model. This model consist in introduction of a constrain to the distribution of long-range connections. We associate his constrain to a possible cost involved in the process of adding new long-range connections to the network. We studied how this cost constrain affects the navigation through the system, taking as a basis for comparison the work of Kleinberg for navigation with local knowledge, and our results conserning for navigation with global knowledge.