Understanding the structure and the dynamics of networks is of paramount importance for many scientific fields that rely on network science. Complex network theory provides a variety of features that help in the evaluation of network behavior. However, such analysis can be confusing and misleading as there are many intrinsic properties for each network metric. Alternatively, Information Theory methods have gained the spotlight because of their ability to create a quantitative and robust characterization of such networks. In this work, we use two Information Theory quantifiers, namely Network Entropy and Network Fisher Information Measure, to analyzing those networks. Our approach detects non-trivial characteristics of complex networks such as the transition present in the Watts-Strogatz model from k-ring to random graphs; the phase transition from a disconnected to an almost surely connected network when we increase the linking probability of Erdős-Rényi model; distinct phases of scale-free networks when considering a non-linear preferential attachment, fitness, and aging features alongside the configuration model with a pure power-law degree distribution. Finally, we analyze the numerical results for real networks, contrasting our findings with traditional complex network methods. In conclusion, we present an efficient method that ignites the debate on network characterization.

Summary This article serves two purposes. Firstly, it surveys the Bandt and Pompe methodology for the statistical community, stressing topics that are open for research. Secondly, it contributes towards a better understanding of the statistical properties of that approach for time series analysis. The Bandt and Pompe methodology consists of computing information theory descriptors from the histogram of ordinal patterns. Such descriptors lie in a 2D manifold: the entropy–complexity plane. This article provides the first proposal of a test in the entropy–complexity plane for the white noise hypothesis. Our test is based on true white noise sequences obtained from physical devices. The proposed methodology provides consistent results: It assesses sequences of true random samples as random (adequate test size), rejects correlated and contaminated sequences (sound test power) and captures the randomness of generators previously analysed in the literature.

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Vehicular networks can be studied using vehicle's behavior individually varying with time, characterized by displacement or velocities. However, on this work we analyze the aggregated graph-based representation, which describes a global aspect of the network, encapsulating the dynamics of each vehicle during a sampled period, thus, verifying its structural behavior with Information Theory quantifiers for mapping these data onto a Complexity-Entropy plane. This method was applied to 17 vehicular networks, varying synthetically its topologies in V2V, V2I and V2V2I, such way its graphs presented a variable dynamic between Watts-Strogatz and Barabási-Albert models behaviors.

Este trabalho propõe um algoritmo de redução do fluxo de dados baseado no comportamento de séries temporais no plano Complexidade-Entropia para redes de sensores sem fio (RSSF). A variação da dinâmica do sistema é identificada em tempo real através de um delimitador construı́do dentro do plano, denominado Ponto de Corte de Complexidade Máxima. Assim, podemos determinar em quais instantes se deve atualizar o intervalo de amostragem, de modo a maximizar a complexidade estatı́stica da amostra de dados resultante. Este método foi aplicado a uma base de dados caóticos e os resultados obtidos foram comparados com os de outros algoritmos de amostragem, apresentando melhor desempenho nas métricas de estatı́stica avaliadas.