Data Mining in Complex Networks: Missing Link Prediction and Fuzzy Communities

This dissertation is devoted to networks: complex interconnected systems where the individual components are connected by binary links arranged in seemingly random but intrinsically structured patterns. Networks are used to model various real-world phenomena ranging from protein interaction in living organisms to the large-scale organisation of human society or the structure of technological networks such as software systems or the Internet. The first part of the dissertation studies a stochastic graph model, which can be considered as a possible extension of Erdős–Rényi random graphs. I discuss some basic statistical properties of the model and devise methods to find the best fit of the model to a given network instance. I also demonstrate how the fitted model can be used to predict previously unknown connections in the network. The second part of the dissertation studies overlapping communities (i.e., dense subgraphs) in sparse networks. I introduce a method based on the concept of fuzzy partition matrices and vertex similarity to uncover meaningful communities with possible overlaps and to identify bridge vertices that belong to more than one community significantly. Finally, I present applications of the link prediction and community detection methods on real-world datasets.