MODELING THE STRUCTURE OF SOCIAL NETWORKS BY USING THE PYTHAGOREAN SPIRAL

摘要

Since the good representation of the complex networks structure can effectively communicate more information and can help explore them and understand their behaviors, the purpose of this paper is to present and model the structure of social networks. Mathematical concepts can be a powerful tool for modeling. However, complex networks in the real world are far too complicated to model in their entirety. Therefore, it is important to identify the information that the generated model may help illustrate. In the present work, we use the spiral of Pythagoras and a combination of mathematical concepts in pre-topology, graph theory and fuzzy logic to generate two different models: the Rings Model and the Member-ship Matrix. The first proposed model has a geometric representation which makes all the nodes visible and every direct link between two nodes illustrates the number of, direct and indirect, paths that connect them and the cost of each one. The second proposed model is a matrix where every column depicts the relation between the corresponding node and the rest of the network. The most important benefit of the models presented in this paper is that they allow the human eye to get information about the strength of connection between the nodes, of complex networks, in an easy and fast way.