Lectures related to Subgraphs vs Induced Subgraphs

Minimum Spanning Trees: Prim's Algorithm

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

Graph Algorithms II: Traversal and Paths

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

Graph Theory and Network Flows

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

Graphs: Properties and Representations

Covers graph properties, representations, and traversal algorithms using BFS and DFS.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Convergence of Random Walks

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Graphs and Networks: Basics and Applications

Introduces the basics of graphs and networks, covering definitions, paths, trees, flows, circulation, and spanning trees.

Graph Theory: Connectivity and Properties

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

Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Expander Graphs: Properties and Eigenvalues

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

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.

Soft Graphs and Subgraphs

Covers soft graphs and induced subgraphs in graph theory.

Connectivity in Graph Theory

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

Fixed Points in Graph Theory

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

Minimal Spanning Tree

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

Graph Algorithms: Modeling and Representation

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

Distances and Motif Counts

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.

Shortest Path Algorithms: BFS and Dijkstra

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

Graph Coloring: Basics and Applications

Covers the basics and applications of graph coloring, including balancing vectors and achieving perfect fairness.

Statistical Analysis of Network Data

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.