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: \textit{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 ($g=0.70\pm0.07$) across all the universities and institutions of the world, while for the journals we find $g=0.65\pm0.15$ 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 $0.75\pm0.05$ for different universities and institutions across the world and around $0.77\pm0.10$ 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.