Lectures related to Introduction to Graph Theory

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

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

Graph Theory: Connectivity and Properties

Explores the properties of undirected and directed graphs, emphasizing connectivity and network topology modeling.

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

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

Soft Graphs and Subgraphs

Covers soft graphs and induced subgraphs in graph theory.

Max Flav-Min Cut in Directed Graphs

Covers the concept of maximum flow-minimum cut in directed graphs with capacity constraints.

Statistical analysis of network data

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

Interlacing Families and Ramanujan Graphs

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

Fixed Points in Graph Theory

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Shortest Path Algorithms: BFS and Dijkstra

Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.

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.

Graph Algorithms II: Traversal and Paths

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Flow Networks: Understanding Flows and Cuts in Algorithms

Covers flow networks, focusing on flows, cuts, and their applications in algorithms.

Networked Control Systems: Opportunities

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

Expander Graphs: Properties and Eigenvalues

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Interlacing Families and Ramanujan Graphs

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

Belief Propagation

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

Connectivity in Graph Theory

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

Probabilistic method and its applications

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

Minimum Spanning Trees: Prim's Algorithm

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