Lecture
This lecture covers the concept of directed networks, where relationships are asymmetric, and examples include social networks, email communications, and powerline networks. It also explores in-degree and out-degree, degree-based models, and the directed stochastic block model. Additionally, the lecture delves into hypergraphs, which generalize graphs by allowing edges to connect any subset of nodes, not just pairs. It explains the basic definitions of hypergraphs, such as vertex sets, edge sets, incident vertices, and degrees. Various examples from computer science, genetics, sociology, and healthcare are provided to illustrate the application of hypergraphs in different fields.