Pareto graphs - Rey, Andrea Alejandra (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
It is well-known that Pareto distribution and related generalizations have historically been considered suitable for modeling income and wealth distributions, among other fields. Nowadays, graphs can be used to model many types of relations and processes in physical, biological, social, and information systems. By combining both concepts, this paper introduces the notion of the Pareto graph and gives some sufficient conditions to determine the existence of a giant component. A simulation study is carried out to evaluate the performance of Pareto random graph generation. In addition, basic graph properties of this novel kind of graph are contrasted with well-known models for random graph generation. The results are applied to real-life data that come from social networks, under the assumption that the degree distribution is well fitted by a Generalized Pareto distribution and compared with the fitting by other heavy-tailed distributions.