A proposal for the EI index for fuzzy groups

Abstract

In this paper, it is proposed a measure that quantifies the relational structure within and between groups that comprehend not only the analysis of disjoint groups or non-disjoint groups but also in fuzzy groups. This measure is based on the existing measure known as the 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. The new measure permits the expansion of the analysis of social networks, for several types of attributes, and thus generating previously untapped knowledge. Moreover, it is also proposed combining edges' and nodes' weights in the evaluation of the EI index. The new measure is tested in two networks in different contexts. The first one is a co-authorship network, where researchers, actors in the network, are divided according to the time of completion of the doctorate. The second network is formed by trade relations between countries of the American continent, where countries are grouped according to the Human Development Index.