Inequality in societies, academic institutions and science journals: Gini and k-indices

Social inequality is traditionally measured by the Gini-index (g). The g-index takes values from 0 to 1 where g=0 represents complete equality and g=1 represents complete inequality. Most of the estimates of the income or wealth data indicate the g value to be widely dispersed across the countries of the world: g values typically range from 0.30 to 0.65 at a particular time (year). We estimated similarly the Gini-index for the citations earned by the yearly publications of various academic institutions and the science journals. The ISI web of science data suggests remarkably strong inequality and universality (g=0.70±0.07) across all the universities and institutions of the world, while for the journals we find g=0.65±0.15 for any typical year. We define a new inequality measure, namely the k-index, saying that the cumulative income or citations of (1−k) fraction of people or papers exceed those earned by the fraction (k) of the people or publications respectively. We find, while the k-index value for income ranges from 0.60 to 0.75 for income distributions across the world, it has a value around 0.75±0.05 for different universities and institutions across the world and around 0.77±0.10 for the science journals. Apart from above indices, we also analyze the same institution and journal citation data by measuring Pietra index and median index.