The Gini-Exposure index for measuring segregation in networks

This paper studies the inequality in the distribution of social interaction profiles among individuals. An interaction profile assigns the probabilities that one individual has to interact with well defined social groups and it can be inferred, for instance, from observations of social ties through networks data. This paper proposes an indicator, the Gini Exposure index, that allows to ranks all the in-between configurations according to the level of inequality in interaction profiles they exhibit. The Gini Exposure index extends the well-known inequality Gini coefficient to the multi-variate setting and applies it in a specific context where inequality in interaction profiles, and not incomes or resources, is the focus. One key advantage of this index is that overall segregation can be decomposed into the segregation experienced by every individual with respect to other people in his own group (isolation) or in other groups (exposure). An empirical analysis of interaction patterns of natives and immigrants across Italian municipalities reveals connections and differences with other exposure measures.