Module 6: Graph Theory & Algorithms

Course Navigation

Graphs, traversal, and shortest paths

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4-5 hours

Foundations of DSA

Memory & Efficiency

Arrays & Memory Fundamentals

Stacks & Queues

Linked Lists

Trees & Hierarchical Structures

Graph Theory & AlgorithmsCurrent

Hash Tables & Hashing

Dynamic Programming

Sorting & Searching

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Section 4 of 4

Module Stats

Total Sections:4

Estimated Time:4-5 hours

Difficulty:Advanced

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Graph Fundamentals Graph Traversal Shortest Paths Graph Applications

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90 minutes

Graph Applications

Explore real-world applications where graphs solve complex problems

Interactive Applications

Social Network Analysis

Find mutual friends, suggest connections, and analyze influence.

Graph Type: Undirected, Unweighted

Key Algorithms: BFS, Connected Components

Metrics: Centrality, Clustering Coefficient

Social Network Graph

Node size represents connection count (influence)

Major Application Categories

Web & Internet

• Web crawling and indexing
• PageRank algorithm
• Link analysis
• Internet routing protocols
• DNS resolution

Social Networks

• Friend recommendations
• Community detection
• Influence propagation
• Social media analytics
• Network visualization

Transportation

• GPS navigation
• Traffic optimization
• Route planning
• Public transit systems
• Supply chain logistics

Computer Science

• Compiler design
• Dependency resolution
• Database query optimization
• Circuit design
• Operating system scheduling

Biology & Chemistry

• Protein structure analysis
• Gene regulatory networks
• Drug discovery
• Molecular interactions
• Phylogenetic trees

Business & Finance

• Fraud detection
• Risk assessment
• Market analysis
• Organizational structures
• Project dependencies

Advanced Graph Problems

NP-Hard Graph Problems

Traveling Salesman Problem (TSP)

Find shortest route visiting all cities exactly once

Graph Coloring

Assign colors to vertices so no adjacent vertices share colors

Maximum Clique

Find largest complete subgraph

Hamiltonian Path

Find path visiting each vertex exactly once

Efficiently Solvable Problems

Minimum Spanning Tree

Kruskal's or Prim's algorithm - O(E log V)

Maximum Flow

Ford-Fulkerson algorithm - O(E²V)

Bipartite Matching

Hungarian algorithm - O(V³)

Strongly Connected Components

Tarjan's algorithm - O(V + E)

Industry Case Studies

Google PageRank

Revolutionary algorithm that ranks web pages based on link structure, treating the web as a massive directed graph.

Graph Model:

Web pages as nodes, hyperlinks as edges

Algorithm:

Random walk with damping factor

Facebook Social Graph

Manages billions of users and their relationships, enabling friend suggestions, news feed ranking, and targeted advertising.

Scale:

3+ billion nodes, 200+ billion edges

Applications:

Recommendations, privacy, community detection

Ride-sharing Route Optimization

Real-time route planning considering traffic, driver locations, and passenger destinations using dynamic graph algorithms.

Challenge:

Dynamic weights, real-time updates

Solution:

Modified Dijkstra's with heuristics

Shortest Paths