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10 Modules / ~100 pages
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Graph Algorithms and Applications
( 24 Modules )

Module #1
Introduction to Graph Theory
Defining graphs, types of graphs, graph representation, and basic graph terminology
Module #2
Graph Traversal Algorithms
Breadth-First Search (BFS) and Depth-First Search (DFS) algorithms, implementation, and applications
Module #3
Shortest Paths Algorithms
Dijkstras algorithm, Bellman-Ford algorithm, and Floyd-Warshall algorithm for finding shortest paths in weighted graphs
Module #4
Minimum Spanning Tree Algorithms
Kruskals algorithm and Prims algorithm for finding minimum spanning trees in weighted graphs
Module #5
Topological Sort and Strongly Connected Components
Topological sort algorithm and strongly connected components in directed graphs
Module #6
Graph Connectivity and Biconnectivity
Algorithms for finding connected components, biconnected components, and articulation points in graphs
Module #7
Network Flow Algorithms
Ford-Fulkerson algorithm, Edmonds-Karp algorithm, and Dinics algorithm for solving maximum flow problems
Module #8
Matching Algorithms
Bipartite matching, Hopcroft-Karp algorithm, and stable marriage problem
Module #9
Graph Coloring and Independent Sets
Graph coloring algorithms, chromatic number, and independent sets in graphs
Module #10
Clique and Cluster Detection
Algorithms for finding cliques, clusters, and community structure in graphs
Module #11
Graph Isomorphism and Automorphism
Algorithms for testing graph isomorphism and automorphism
Module #12
Random Graph Models
Erdős-Rényi model, small-world networks, and preferential attachment models
Module #13
Graph Visualization and Drawing
Algorithms and techniques for visualizing and drawing graphs
Module #14
Social Network Analysis
Centrality measures, community detection, and epidemic spread in social networks
Module #15
Web Graph Analysis
Structural properties of the web graph, PageRank, and web crawling
Module #16
Recommendation Systems
Collaborative filtering, content-based filtering, and graph-based recommendation systems
Module #17
Biological Network Analysis
Protein-protein interaction networks, gene expression networks, and biological network analysis
Module #18
Traffic Network Analysis
Traffic flow, traffic assignment, and traffic network optimization
Module #19
Scheduling and Resource Allocation
Graph-based scheduling algorithms and resource allocation problems
Module #20
Computational Complexity of Graph Algorithms
NP-completeness, hardness of approximation, and efficient algorithms for graph problems
Module #21
Approximation Algorithms for Graph Problems
Approximation algorithms for NP-hard graph problems, such as vertex cover and traveling salesman
Module #22
Online and Dynamic Graph Algorithms
Algorithms for dynamic graphs, online algorithms, and streaming graph algorithms
Module #23
Distributed Graph Algorithms
Algorithms for distributed graph processing, parallel algorithms, and distributed graph systems
Module #24
Course Wrap-Up & Conclusion
Planning next steps in Graph Algorithms and Applications career


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