🔥 minimum spanning tree → MST relies on graph-theoretic concepts—vertices/edges, weighted undirected connected graphs, trees, cuts, cycles, and connectivity—which define the problem and justify algorithms like Kruskal’s and Prim’s and their correctness.

🔥 prim algorithm → Prim's algorithm relies on graph-theory concepts—vertices/edges, weighted undirected graphs, connectivity, spanning trees, and MST cut/cycle properties—to define the problem, select safe edges, and prove correctness.

🔥 kruskal algorithm → Kruskal's algorithm operates on weighted, undirected graphs and depends on graph-theoretic concepts—vertices, edges, weights, connectivity, spanning trees, and cut/cycle properties—for its procedure and correctness.

🔥 markov chain → Markov chains can be modeled as directed, weighted graphs where states are nodes and edges carry transition probabilities; graph-theoretic concepts like strong connectivity (irreducibility), cycles/periods, path enumeration, and spectral properties of adjacency/transition matrices underpin analysis of multi-step behavior and convergence to stationary distributions.

🌟 depth first search →

🌟 breadth first search →

⚡️ pagerank →