Facebook Social Graph: Structure and Small-World Phenomenon

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Related lectures (31)

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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

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

Belief Propagation

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Shortest Paths: Negative Weights

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

Connectivity in Graph Theory

Covers the fundamentals of connectivity in graph theory, including paths, cycles, and spanning trees.

Cheeger's Inequalities

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

Cavity Method: Mean Field Theory

Explores the Cavity Method in Mean Field Theory, analyzing spins in an external field within a graph.

Dijkstra's Algorithm Overview

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

Assembly: Physics of Manufacturing

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

Minimum Spanning Trees: Prim's Algorithm

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.