A proposal for the EI index for fuzzy groups

Abstract

In this article, a measure that quantifies the relational structure within and between groups is proposed, comprising not only the analysis of disjoint or non-disjoint groups, but also of fuzzy groups. This measure is based on the existing measure known as EI index. The current EI index is a measure of homophily applied to networks with the presence of disjoint groups, although disjoint groups on a large scale rarely exist in many empirical networks. In addition, the combination of edge and node weights in the evaluation of the EI index is also proposed. We tested the measure in two networks in different contexts. The first is a co-authorship network, where researchers, actors in the network, are divided according to the time of Ph.D. completion. The second network is formed by trade relations between countries of the American continent, where countries are grouped according to the Human Development Index. The application of the proposed measure in these two networks is justified by the imprecision of the information or by the difficulty of allocating nodes in a specific group, being necessary to define affiliation levels. Therefore, the new measure allows expanding the analysis of social networks, for different types of attributes, thus generating previously unexplored knowledge.