Shortest Paths: Negative Weights & Applications

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Introduces Dijkstra's algorithm and probabilistic analysis through the Hiring Problem.

Explores the properties of trees in graph theory, focusing on nodes, paths, cycles, and the characterization of trees in a directed graph.

Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.

Explores Bellman-Ford algorithm for negative weight graphs and currency exchange rates.

Covers flow networks, focusing on flows, cuts, and their applications in algorithms.

Introduces the basics of graph algorithms, covering traversal, representation, and data structures for BFS and DFS.

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Explores graph coloring, directed cycles, LLL algorithm applications, and element dependencies in graphs.