Graphs and Networks: Basics and Applications

This lecture covers the basics of graphs and networks, starting with definitions of graphs, vertices, and edges in undirected graphs. It then progresses to discussing paths, cycles, and trees in graphs, along with concepts like handshake lemma and directed graphs. The lecture further delves into network graphs, exploring weights, capacities, flows, and flow conservation laws. It also touches upon feasible flows, circulation, and the use of matrices to represent network flows. The importance of spanning trees and their relation to the incidence matrix is also explained, emphasizing their role in network analysis.