Convergence of Random Walks

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

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Covers the basics of graph algorithms, focusing on modeling and representation of graphs in memory.

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Discusses the Ford-Fulkerson method and strongly connected components in graph algorithms.

Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.