Concept

Neighbourhood (graph theory)

Related lectures (27)

Seifert van Kampen: demonstration and relationship with rectangles

Covers the demonstration of Seifert van Kampen theorem and the relationship with rectangles and paths.

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Polygonal Presentations: Classification of Surfaces

Explores the classification of surfaces based on polygonal presentations and the identification of sides and vertices.

Spatial relations and topology: summary

Covers spatial relations in general, focusing on topology and its role.

Graph Theory Fundamentals

Explores fundamental graph theory concepts, Erdős' results, Chromatic Lemma, and Union Bound theorem in graph theory.

Graph Representation and Traversal

Introduces graph theory basics, graph representation methods, and traversal algorithms like BFS and DFS.

Epidemic Spreading Models

Covers classical models of epidemic spreading and dynamics on networks with examples.

Social Dynamics of Contagion and Discovery

Explores the social dynamics of adoption and contagion on complex networks, emphasizing the emergence of novelties and the impact of social interactions.

Regular Graphs: Self-complementary

Covers regular and self-complementary graphs, exploring their properties and examples.

Spatial relations and topology

Covers spatial relations and topology in GIS, emphasizing the importance of topological consistency in spatial analysis.

Union and Join Operations

Explores the union and join operations on graphs, illustrating their definitions and properties.

Unlabeled Trees Estimation

Explores the estimation of unlabeled trees and their unique reconstruction from sequences.

Sparsest Cut: Bourgain's Theorem

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Depth-First Search: Traversing and Sorting Graphs

Explores depth-first search, breadth-first search, graph representation, and topological sorting in graphs.

Solving Linear Programs: SIMPLEX Method

Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.

Graph Algorithms: Modeling and Representation

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

Belief Propagation

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

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Graph Theory Fundamentals

Covers the fundamentals of graph theory, including vertices, edges, degrees, walks, connected graphs, cycles, and trees, with a focus on the number of edges in a tree.

Introduction to Graph Theory

Covers the basics of graph theory, including network flows, degrees of vertices, walks, and subgraphs.