In this work, we present a methodology to identify COVID-19 spreaders using the analysis of the relationship between socio-cultural and economic characteristics with the number of infections and deaths caused by the COVID-19 virus in different countries. For this, we analyze the information of each country using the complex networks approach, specifically by analyzing the spreaders countries based on the separator set in 5-layer multiplex networks. The results show that, we obtain a classification of the countries based on their numerical values in socioeconomics, population, Gross Domestic Product (GDP), health and air connections; where, in the spreader set there are those countries that have high, medium or low values in the different characteristics; however, the aspect that all the countries belonging to the separator set share is a high value in air connections. INDEX TERMS Complex networks, complex systems, COVID-19, multiplex networks, optimization, social networks.

We study the correlation properties of word lengths in large texts from 30 ebooks in the English language from the Gutenberg Project (www.gutenberg.org) using the natural visibility graph method (NVG). NVG converts a time series into a graph and then analyzes its graph properties. First, the original sequence of words is transformed into a sequence of values containing the length of each word, and then, it is integrated. Next, we apply the NVG to the integrated word-length series and construct the network. We show that the degree distribution of that network follows a power law, P (k) ∼ k −γ , with two regimes, which are characterized by the exponents γ s ≈ 1.7 (at short degree scales) and γ l ≈ 1.3 (at large degree scales). This suggests that word lengths are much more strongly correlated at large distances between words than at short distances between words. That finding is also supported by the detrended fluctuation analysis (DFA) and recurrence time distribution. These results provideEntropy 2015, 177799 new information about the universal characteristics of the structure of written texts beyond that given by word frequencies.

No abstract

Inverse percolation is known as the problem of finding the minimum set of nodes whose elimination of their links causes the rupture of the network. Inverse percolation has been widely used in various studies of single-layer networks. However, the use and generalization of multiplex networks have been little considered. In this work, we propose a methodology based on inverse percolation to quantify the robustness of multiplex networks. Specifically, we present a modified version of the mathematical model for the multiplex-vertex separator problem (m-VSP). By solving the m-VSP, we can find nodes that cause the rupture of the mutually connected giant component (MCGC) and the large viable cluster (LVC) when their links are removed from the network. The methodology presented in this work was tested in a set of benchmark networks, and as case study, we present an analysis using a set of multiplex social networks modeled with information about the main characteristics of the best universities in the world and the universities in Mexico. The results show that the methodology presented in this work can work in different models and types of 2- and 3-layer multiplex networks without dividing the entire multiplex network into single-layer as some techniques described in the specific literature. Furthermore, thanks to the fact that the technique does not require the calculation of some structural measure or centrality metric, and it is easy to scale for networks of different sizes.

No abstract