Centralisation in Financial, Socio-Economic and Ecological Complex Networks

Abstract

This thesis is composed of five research papers I’ve co-authored with my supervisor, i.e. Professor Didier Sornette and my co-supervisor, i.e. Professor Claudio J. Tessone. While two of the papers constituting this thesis have been published in peer-reviewed journals, the other three are currently under submission. The present thesis focuses on the analysis of centralisation in ecological, economic, financial and social networks. The first two parts of the thesis are devoted to analyse centralisation in the Bitcoin ecosystem. We consider the Bitcoin Lightning Network (BLN) for 18 months since its launch in January 2018 and analyse its binary and weighted representation at the micro-, meso-, and macro-scale. The results show that the bitcoin distribution in the BLN is strongly uneven: the average Gini coefficient of users’ bitcoins is 0.88, reflecting that 10% of the users hold 80% of the bitcoins in the BLN. The increasing unevenness of the bitcoin distribution is further confirmed by the evolution of the Gini coefficient of the centrality measures and by the evidence that the BLN meso-scale structure becomes increasingly compatible with a core-periphery structure. In the third part of the thesis, we present a novel model for the emergence of collective dynamics in financial markets using an Ising-like model on non-normal networks. Our model has its foundations in the intrinsic asymmetry and hierarchy of social influence that, in turn, can be represented by non-normal networks. The influential nodes in non-normal networks have a large influence on other nodes through directed links. Social imitation and herding that start from the influential nodes’ opinions lead to transient dynamics that induce financial bubbles and crashes. Via analytical results, agent-based simulations, and empirical analysis of financial data, we show that financial bubble size is proportional to the Kreiss constant which characterizes the degree of non-normality of the network. The results of the first three parts of the thesis show that influential nodes play a signifi- cant role in the centralisation of the Bitcoin ecosystem as well as in the formation of bubbles in financial systems. Thus, in the fourth part of the thesis, we propose a dynamic Markov process (DMP) to identify influential nodes in complex networks. This method integrates the Markov chain and the spreading dynamics to rank the influence of nodes. Numerical results indicate that the DMP method can accurately evaluate the influence of nodes for both single and multi-spreaders. In the last part of the thesis, we explore the fitness-complexity algorithm for the nestedness maximization problem. Nestedness refers to a hierarchical network structure where the set of neighbors of a given node is a subset of the neighbors of better-connected nodes. Nestedness maximization aims at sorting the rows and columns of the adjacency matrix to maximize the level of nestedness of the network. By analysing the ecological networks and World Trade country-product networks, we show that the fitness-complexity algorithm is highly effective to achieve the nestedness maximization task.