Undirected and directed graphs of interest are real-world networks, model-generated graphs and various induced graphs (such as line graphs and motif networks). Networks and graphs are characterized, analyzed and categorized by combinatorial, algebraic and probabilistic measures of connectivity and centrality, via matrix representation, connection and computation (including graph Laplacian matrices). Probabilistic network models include the small-world model, the scale-free model as well as the traditional Erdos–Rényi model. Community detection methods are introduced. Prerequisites: linear algebra, multivariable calculus, and basic programming knowledge and skill.
Department of Computer Science