Quantifying intragroup and intergroup connections in non-disjoint groups in social networks: A comprehensive analysis incorporating edges' and nodes' weights

Abstract

In this paper, we propose generalizations of the EI index to quantify the distinction between intragroup and intergroup connections in social networks. These generalizations enable the analysis of interactions between non-disjoint groups, as large-scale disjoint groups are rarely found in many empirical networks. By expanding social network analysis, these measures facilitate the identification of actors with greater similarities or differences, generating previously untapped knowledge. Furthermore, we propose incorporating both edges' and nodes' weights in assessing the EI index. Intuitively, our approach classifies each network edge as internal or external, depending on the attribute groups that each node linked by the given edge belongs to. Since nodes can belong to more than one attribute group, three methods of classifying a network edge are proposed which depend on the number of shared groups by the pair of nodes. We evaluate the new measures in two distinct network contexts. The first context involves a co-authorship network, where researchers, acting as network actors, are categorized based on their respective areas of expertise in management engineering. The second network consists of trade relations among countries in the Americas, with countries grouped according to their participation in trade agreements. The analysis showed which area of management engineering is more independent by having more internal connections and made it possible to investigate the role of trade agreements in the actual trades made by countries. These proposals provide a more comprehensive and nuanced understanding of network dynamics, allowing for a more precise comprehension of interactions and patterns present in social systems.