Graph Theory: Connectivity and Properties

This lecture covers the properties of undirected and directed graphs, including basic definitions, neighbors of a node, subgraphs, connectivity, paths, cycles, trees, and digraphs. It explains the concepts of connectivity, completeness, sources, sinks, directed trees, weak/strong connectivity, global reachable nodes, and directed spanning trees. The instructor emphasizes the importance of graph theory in modeling control network topology and discusses open problems related to graph connectivity and achieving consensus.