Efeito da amostragem nas propriedades topológicas de redes complexas (original) (raw)

Abstract

Several natural or human made complex systems can be represented by complex networks-a theory which integrates the study of graphs with statistical mechanics. This kind of representation, however, can be biased by the way in which the data is obtained. In general, the data used to represent such systems is not always accurate, as in the case of the World Wide Web (WWW). Therefore, even if the sampled networks are large, their properties are directly affected by the way in which they were obtained and may not correspond to those of their respective original networks. For instance, the most used sampling methodology for capturing routers of the Internet, if performed on random networks, tends to obtain scale-free networks as results. On the other hand, sampled scale-free networks are not guaranteed to have this property. Because of these and other problems which may occur during the network sampling, it is very important to evaluate the variation of the network properties with respect to noise (in order to know which of them have less variation, being therefore more suitable for the characterization of networks with sampling problems) and the effect of sampling in the characterization, classification, and analysis of complex networks. In this work, we investigated the effect of three types of perturbations (noise), namely, edge addition, removal, and rewiring on the respectively estimated complex network properties, and the most suitable properties to characterize sampled networks were identified. Furthermore, two novel structures in complex networks were defined, namely, border trees and chains of vertices, which are possibly related to sampling. The occurrence of these structures in poorly-sampled networks was found to be high, implying a relation with partially sampled networks. In order to investigate such a hypothesis, the presence of chains of vertices was investigated in networks which were gradually sampled by random walks.

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