Advanced Graph Algorithms Questions

Higher level and combined graph algorithm topics frequently expected at senior or competitive programming levels. Topics include strongly connected components and algorithms such as Kosaraju and Tarjan, minimum spanning trees using Kruskal and Prim with Union Find optimizations, network flow fundamentals including Ford Fulkerson and Edmonds Karp and applications to bipartite matching, graph reductions and transformations, graph coloring and bipartite checks, advanced traversal techniques such as bidirectional search and multi source traversals, and strategies to combine algorithms for complex problems. Emphasize time and space complexity, algorithm correctness proofs, implementation pitfalls, and when to prefer one algorithm or data structure over another.