A set of new inequality indexes are constructed to measure the relative unbalanced difference between regions or groups of elements in a geographical systems. Firstly, the within-group inequality index, namely, the Gini coefficient based on the Lorenz curve, is transformed into a new mathematical expression. Then, based on the new formula, the within-group index is generalized to between-group inequality index. Technically, the two types of inequality indexes can be integrated into the same logic framework. As an example, the new formulae are applied to three systems of cities in China, including Beijing-Tianjin-Hebei region, Yangtze River Delta, and Pearl River Delta. The results display a spatio-temporal evolution patterns of relative mean differences within and between these urban systems.

%U https://xbna.pku.edu.cn/EN/10.13209/j.0479-8023.2019.107