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Master's Dissertation
DOI
10.11606/D.55.2016.tde-04102016-145152
Document
Author
Full name
Eduardo Zorzo Sartoretto
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Nonato, Luis Gustavo (President)
Coletti, Cristian Favio
Gallo, Alexsandro Giacomo Grimbert
Silva, Tiago Pereira da
Title in Portuguese
Conectividade para um modelo de grafo aleatório não homogêneo
Keywords in Portuguese
Conectividade de grafos
Grafos aleatórios
Modelo de Erdös-Rényi
Abstract in Portuguese
A caracterização de redes e o estudo de sistemas, ambos utilizando grafos, é algo muito usado por várias áreas científicas. Uma das linhas deste estudo é denominada de grafos aleatórios, que por sua vez auxilia na criação de modelos para análise de redes reais. Consideramos um modelo de grafo aleatório não homogêneo criado por Kang, Pachón e Rodríguez (2016), cuja construção é feita a partir da realização do grafo binomial G(n; p). Para este modelo, estudamos argumentos e métodos usados para encontrar resultados sobre o limiar de conectividade, importante propriedade relacionada a existência assintótica de vértices e componentes isolados. Em seguida, constatamos algumas características positivas e negativas a respeito da utilização do grafo para modelar redes reais complexas, onde usamos de simulações computacionais e medidas topológicas.
Title in English
Connectivity to an inhomogeneous random graph model
Keywords in English
Connectivity threshold of graphs
Erdös-Rényi model
Random graphs
Abstract in English
The characterization of networks and the study of systems, both using graphs, is very used by several scientific areas. One of the lines of this study is called random graphs, which in turn assists in creating models for the analysis of real networks. We consider an inhomogeneous random graph model created by Kang, Pachón e Rodríguez (2016), where its construction is made from the realization of the binomial graph G(n; p). For this model, we studied the arguments and methods used to find results on the connectivity threshold, important property related to asymptotic existence of vertices and isolated components. Then we found some positive and negative characteristics about the use of the graph to model complex real networks, using computer simulations and topological measures.
 
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Publishing Date
2016-10-04
 
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