The Zipf-Polylog distribution: Modeling human interactions through social networks

The Zipf distribution attracts considerable attention because it helps describe data from natural as well as man-made systems. Nevertheless, in most of the cases the Zipf is only appropriate to fit data in the upper tail. This is why it is important to dispose of Zipf extensions that allow to fit the data in its entire range. In this paper, we introduce the Zipf-Polylog family of distributions as a two-parameter generalization of the Zipf. The extended family contains the Zipf, the geometric, the logarithmic series and the shifted negative binomial with two successes, as particular distributions. We deduce important properties of the new family and demonstrate its suitability by analyzing the degree sequence of two real networks in all its range.Peer ReviewedPostprint (author's final draft

Complexity in Economic and Social Systems

There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure

Using the Marshall-Olkin extended Zipf distribution in graph generation

Being able to generate large synthetic graphs resembling those found in the real world, is of high importance for the design of new graph algorithms and benchmarks. In this paper, we first compare several probability models in terms of goodness-of-fit, when used to model the degree distribution of real graphs. Second, after confirming that the MOEZipf model is the one that gives better fits, we present a method to generate MOEZipf distributions. The method is shown to work well in practice when implemented in a scalable synthetic graph generator.Peer ReviewedPostprint (published version