Adjacency Matrices for Loops, Digraphs & Multigraphs | Discrete Mathematics §10.3

The clean symmetric matrix of a simple graph is only the start. Add loops, parallel edges, or direction and the matrix changes shape — and which representation you should pick depends entirely on how dense the graph is. In this video: adjacency matrices beyond simple graphs, on the board. For a pseudograph a loop puts a one on the diagonal and parallel edges push entries above one, so it is no longer a zero-one matrix. For a directed graph the matrix is generally not symmetric: row sums give out-degrees, column sums give in-degrees. We finish with the space-time trade-off: a sparse graph is cheaper as adjacency lists (about c·n versus n squared), while a dense graph favors the matrix with its constant-time edge lookup. New here? Start with §10.3 Adjacency Lists and the Adjacency Matrix. This video is part of Discrete Mathematics · Graphs (§10.3 — Representing Graphs & Graph Isomorphism). Full section playlist linked above / in the description on the channel. Made with the Engineering Simplified method: a calm, two-voice story lesson taught on a chalk-and-board, with every definition and example drawn out step by step. Topic coverage follows Rosen, Discrete Mathematics and Its Applications (Chapter 10).