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