The 'complex network' has been studied in many disciplines. In this thesis, we use an economic network to study the heterogeneity of the networks. Networks of shareholders in Turkey and the Netherlands are constructed from raw data. The nodes are shareholders and an edge between shareholders exists if they have invested in the same company.
The general analysis of network has shown that this type of network has characteristics similar to other types of real-world networks: power-law like degree distributions, small-world phenomenon and scaling of community size distributions. Furthermore, we introduce the 'type' of shareholders and analyse the different behaviour of shareholder types by comparing with a randomised null model. The results are that different types of shareholders are parts of different topological structures in the networks.
Based on the economic behaviours, we propose a random walk model to mimic the different roles of shareholders in the networks. The model starts with a directed random graph of shareholders with assigned labels/types mimicing the raw data, and companies, showing which companies shareholders have invested in.
A biased random walker model is introduced to model, on an abstract level, how shareholders' investments evolve. We then extract the associated shareholder network. This evolving model can qualitatively explain general characteristics and heterogeneity of the real-world shareholder networks: the scaling of community size distributions, percolation behaviour and the average shortest paths between different types.
When we focus on the emergence of features from local interactions and higher-order interactions. We propose a new framework for this analysis. For a more general analysis, we design a simple transition matrix of temporal triplets. By comparing the transition matrix of higher-order interactions with the transition matrix of a pairwise interaction toy model, we can quantify the interactions of triplets. Moreover, we create an algorithm based on the transition matrix to make link predictions. We apply this framework to real-world networks and show that this new framework is successful in making predictions.Open Acces
