Communities Detection in Multiplex Networks Using Optimization: Study Case—Employment in Mexico during the COVID-19 Pandemic

The detection of communities in complex networks offers important information about the structure of the network as well as its dynamics. However, it is not an easy problem to solve. This work presents a methodology based of the robust coloring problem (RCP) and the vertex cover problem (VCP) to find communities in multiplex networks. For this, we consider the RCP idea of having a partial detection based onf the similarity of connected and unconnected nodes. On the other hand, with the idea of the VCP, we manage to minimize the number of groups, which allows us to identify the communities well. To apply this methodology, we present the dynamic characterization of job loss, change, and acquisition behavior for the Mexican population before and during the COVID-19 pandemic modeled as a 4- layer multiplex network. The results obtained when applied to test and study case networks show that this methodology can classify elements with similar characteristics and can find their communities. Therefore, our proposed methodology can be used as a new mechanism to identify communities, regardless of the topology or whether it is a monoplex or multiplex network.

Analysis and Characterization of the Spread of COVID-19 in Mexico through Complex Networks and Optimization Approaches

This work analyzes and characterizes the spread of the COVID-19 disease in Mexico, using complex networks and optimization approaches. Specifically, we present two methodologies based on the principle of the rupture for the GC and Newton's law of motion to quantify the robustness and identify the Mexican municipalities whose population causes a fast spread of the SARS-CoV-2 virus. Specifically, the first methodology is based on several characteristics of the original version of the Vertex Separator Problem (VSP), and the second is based on a new mathematical model (NLM). By solving VSP, we can find nodes that cause the rupture of the giant component (GC). On the other hand, solving the NLM can find more influential nodes for the entire system’s development. Specifically, we present an analysis using a coupled social network model with information about the main characteristics of the contagion and deaths caused by COVID-19 in Mexico for 19 months (January 2020–July 2021). This work aims to show through the approach of complex networks how the spread of the disease behaves, and, thus, researchers from other areas can delve into the characteristics that cause this behavior.

Identification of COVID-19 Spreaders Using Multiplex Networks Approach.

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.