Master graph topologies, adjacency architectures, BFS/DFS, DAG topological sorting, Dijkstra, Bellman-Ford, Prim, Kruskal, and DSU.
Formal graph definitions (V, E), directed vs undirected, weighted, cyclic/acyclic, bipartite verification, and Handshaking Lemma.
Adjacency Matrix vs Adjacency List vs Edge List trade-offs, Compressed Sparse Row (CSR) for HPC, and incidence representations.
Breadth-First Search (queue, shortest unweighted path), Depth-First Search (call stack, tree/back/forward edges), and cycle detection.
Linear dependency orderings: Kahn's in-degree BFS algorithm, DFS reverse post-order, and detecting cyclic dependency deadlocks.
Single-source and all-pairs: Dijkstra's greedy min-heap, Bellman-Ford negative edge relaxation and negative cycle detection, and Floyd-Warshall.
Cut property theorem, Prim's greedy vertex expansion, Kruskal's edge sorting, and Disjoint Set Union (DSU) with path compression and rank.