Application of Multivariate Exponential Random Graph Models in Small Multilayer Networks: Latin America, Tariffs, and Importation

This work is framed as an application of static and small exponential random graph models for complex networks in multiple layers. This document revisits the small network and exhibits its potential. Examining the bibliography reveals considerable interest in large and dynamic complex networks. This research examines the application of small networks (50,000 population) for analyzing global commerce, conducting a comparative graph structure of the tariffs, and importing multilayer networks. The authors created and described the scenario where the readers can compare the graph models visually, at a glance. The proposed methodology represents a significant contribution, providing detailed descriptions and instructions, thereby ensuring the operational effectiveness of the application. The method is organized into five distinct blocks (Bn) and an accompanying appendix containing reproduction notes. Each block encompasses a primary task and associated sub-tasks, articulated through a hierarchical series of steps. The most challenging mathematical aspects of a small network analysis pertain to modeling and sample selection ( sel_p ). This document describes several modeling tasks that confirm that sel_p = 10 is the best option, including modeling the edges and the convergence and covariance model parameters, modeling the node factor by vertex names, Pearson residual distributions, goodness of fit, and more. This method establishes a foundation for addressing the intricate questions derived from the established hypotheses. It provides eight model specifications and a detailed description. Given the scope of this investigation, a historical examination of the relationships between different network actors is deemed essential, providing context for the study of actors engaged in global trade. Various analytical perspectives (six), encompassing degree analyses, diameter and edges, hubs and authority, co-citation and cliques in mutual and collapse approaches, k-core, and clustering, facilitate the identification of the specific roles played by actors within the importation network in comparison to the tariff network. This study focuses on the Latin American and Caribbean region.