Two more ways of spelling Gini Coefficient with Applications

In this paper, we draw attention to a promising yet slightly underestimated measure of variability - the Gini coefficient. We describe two new ways of defining and interpreting this parameter. Using our new representations, we compute the Gini index for a few probability distributions and describe it in more detail for the negative binomial distribution. We also suggest the latter as a tool to measure overdispersion in epidemiology

Dynamic random intersection graph: Dynamic local convergence and giant structure.

Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when they share at least one group. We extend this approach and make the communities dynamic by letting them alternate between an active and inactive phase. We analyse the new model, delivering results on degree distribution, local convergence, giant component, and maximum group size, paying particular attention to the dynamic description of these properties. We also describe the connection between our model and the bipartite configuration model, which is of independent interest