Random Graph Models, Network Centralities and Graph Clustering

Talk Abstract: Many real-world complex networks share a number of common properties such as sparsity, heavy-tailed degree distribution, the existence of a giant connected component, small world property and edge transitivity. Firstly, I review several basic random graph models such as Erdos-Renyi random graph, exponential family of random graph models (ERGMs), stochastic block models (SBMs), random geometric graphs, and indicate which model can represent well a given property. Secondly, I describe the main network centrality indices which can be applied to study network structure or to assess network robustness. I conclude with an overview of main methods in graph clustering with a particular emphasis on the methods designed with the help of random graph models and on the methods using centrality indices