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Concept

Component (graph theory)

Related lectures (31)

Phase Transitions: Percolation in 2D Networks

Explores phase transitions through percolation in 2D networks.

Algebraic Graph Theory: Matrices and Connectivity

Explores algebraic graph theory applied to networked control systems and consensus algorithms.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Graph Algorithms: DFS, Topological Sort, SCC

Explores DFS, Topological Sort, SCC in graphs, and introduces Flow Networks with practical examples.

Networks: Trees MOOC: Optimization: principles and algorithms - Network and discrete optimization

Explains the concept of trees in graph theory and the definition of a spanning tree.

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

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

Networked Control Systems: Properties of Laplacian Matrices

Explores Laplacian matrix properties in networked control systems and their relation to graph theory.

Networked Control Systems: Laplacian Flow and Heat Equation

Explores Laplacian flow, heat equation analogies, and microgrid networked controllers.

Minimum Guardians in Graphs

Explores the concept of minimizing guardians in graphs through strategic edge selection.

Non-parametric regression for networks

Explores non-parametric regression for networks, covering object data analysis, network graphs, extrinsic distances, and practical projections.

Graph Theory: Path Weighted by Amplitude

Covers the calculation of paths in a graph, focusing on amplitude-weighted paths.

Networks, Flows MOOC: Optimization: principles and algorithms - Network and discrete optimization

Covers the definition of flow in a network and flow calculation.

Belief Propagation

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

Minimal Spanning Tree

Covers the concept of weighted graphs and the Greedy algorithm for finding a minimal spanning tree.

Networked Control Systems: Opportunities

Explores coordination in networked control systems, graph theory, and consensus algorithms.

Spectral Clustering: Theory and Applications

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

Stochastic Block Model

Covers the Stochastic Block Model and its application in community detection, exploring its mathematical formulation and challenges.

Geometry: Eulerian Circuits

Explores Eulerian circuits through the Königsberg bridges problem, leading to the development of graph theory and topology.

Probabilistic method and its applications

Introduces the probabilistic method to prove existence results in graph theory.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.