Networks: Paths and Components

This lecture covers the concepts of longest simple paths in directed graphs, the finite number of simple paths between nodes, connectivity, equivalence classes, and connected components. It explains how the maximum number of arcs in a simple path is m - 1, and how there is a finite number of simple paths between two nodes in a directed graph. The lecture also discusses strong connectivity between nodes, equivalence classes in graphs, and how connected components are defined as subgraphs with nodes that are connected.