Measuring Inequalities on Social Networks: A Network-based Generalization of the Gini Index

Abstract

We construct a novel inequality index that incorporates a social network structure, and name it the network-based Gini index, as it generalizes the Gini index. We also provide a basic axiomatization of our index, following the approach of Sen(1954): Any social welfare function satisfying Weighting Equity, Independent Monotonicity, Zero Weight on Top, and Ordinal Information must rank income distributions of a given mean link income in precisely the same way as the negative of the network-based Gini indexes of the respective distributions. We also show that the network-based Gini index satises Transfer Monotonicity, Scale Invariance, and Comparability. Finally, we construct the weighted network-based Gini index on weighted networks, and verify that the index has a similar axiomatization result and satises almost the same properties with the network-based Gini index.