Concept
Component (graph theory)
Related lectures (144)
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Prim's and Kruskal's Algorithms
Explores Prim's and Kruskal's algorithms for finding minimum spanning trees in a graph, covering their correctness, implementation, and analysis.
Minimum Spanning Trees
Covers the implementation and analysis of disjoint sets data structure and introduces the concept of minimum spanning trees.
Pseudorandomness: Expander Mixing Lemma
Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.
Open Problems
Explores a variety of open problems in graph theory and computational complexity, challenging students to analyze and solve complex issues.
Facebook Social Graph: Structure and Small-World Phenomenon
Examines the Facebook social graph structure, small-world phenomenon, four degrees of separation, and user homophily.
Shortest Paths: Negative Weights & Applications
Covers Minimum Spanning Trees, Kruskal's Algorithm, and Shortest Paths in directed graphs.
Networked Control Systems: Challenges and Opportunities
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Cheeger's Inequality
Explores Cheeger's inequality and its implications in graph theory.