Module 3: Graph Analysis

In module 3 we turn to graph analysis and introduce various measures to understand network structure and dynamics. We begin with fundamental concepts of connectivity and distance, such as geodesic distance and the Largest Connected Component (LCC). The module then covers global metrics used to describe the entire network, including diameter, average path length, density, and mean degree. Following this, several centrality measures are introduced to quantify node influence of individual nodes. These include Eigenvector Centrality, Katz Centrality, and the distinction between Hubs and Authorities for directed networks. The module also explores the concepts of clustering and transitivity, which measure the tendency of nodes to form dense groups. It concludes with an analysis of network resilience, examining the network's ability to maintain structural integrity during random failures or targeted attacks.