This lecture covers the concepts of strongly connected components (SCC) in digraphs, where a subgraph is considered an SCC if it is strongly connected and cannot be strictly included in a larger SC subgraph. The instructor explains the condensation digraph, which simplifies a digraph by collapsing each SCC into a node. The lecture also discusses the properties of condensation digraphs, consensus algorithms, and the evolution of states in digraphs. Examples and proofs are provided to illustrate the theoretical concepts.