Facebook Social Graph: Structure and Small-World Phenomenon

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Related lectures (31)

Graph Theory and Network Flows Log in to Mediaspace to watch this video

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Sparsest Cut: ARV Theorem Log in to Mediaspace to watch this video

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Graph Theory: Girth and Independence Log in to Mediaspace to watch this video

Covers girth, independence, probability, union bound, sets, and hypergraph recoloring.

Shortest Paths: Negative Weights Log in to Mediaspace to watch this video

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

Cheeger's Inequalities Log in to Mediaspace to watch this video

Explores Cheeger's inequalities for random walks on graphs and their implications.

Dijkstra's Algorithm Overview Log in to Mediaspace to watch this video

Demonstrates the iterative process of applying Dijkstra's algorithm to find optimal paths.

Assembly: Physics of Manufacturing Log in to Mediaspace to watch this video

Discusses the importance of assembly in manufacturing and covers common couplings, stability, and spatial vectors.

Bellman-Ford Algorithm: Analysis and Correctness Log in to Mediaspace to watch this video

Explores the Bellman-Ford algorithm, its correctness, and practical applications in dynamic networks and real-world scenarios.

Interlacing Families and Ramanujan Graphs Log in to Mediaspace to watch this video

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Szemerédi Regularity Lemma Log in to Mediaspace to watch this video

Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.

Interlacing Families and Ramanujan Graphs Log in to Mediaspace to watch this video

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

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