Interactive Graph Theory Learning
Interactive Graph Theory Learning
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Turn real business decisions into optimization models and solve them in Python with free, open-source tools.
Learning Path
Master graph theory through interactive lessons
Available Lessons
Introduction to Graphs
A comprehensive introduction to graph theory fundamentals, covering definitions, terminology, types, theorems, and applications.
Fundamental Structures in Graphs
Explore the essential structures in graphs including paths, walks, trails, cycles, connectivity, components, and the handshaking lemma.
Trees and Their Applications
Explore trees as fundamental graph structures and their wide-ranging applications in computer science, data organization, and real-world systems.
Graph Traversal Algorithms
Master the fundamental graph traversal techniques and their systematic methods for exploring graph structures.
Shortest Path Algorithms
Master the fundamental algorithms for finding shortest paths in weighted graphs, including Dijkstra's, Bellman-Ford, A*, and Floyd-Warshall algorithms.
Minimum Spanning Trees
Learn about minimum spanning trees and the algorithms to find them: Prim's, Kruskal's, and Borůvka's algorithms.
Graph Connectivity and Components
A comprehensive exploration of graph connectivity, components, and their applications in network analysis and system design.
Network Flow Algorithms
Master network flow problems including maximum flow, minimum cut, and their applications in optimization and resource allocation.
Shortest Path Algorithms
Key Concepts:
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Shortest Path Algorithms
Master the fundamental algorithms for finding shortest paths in weighted graphs, including Dijkstra's, Bellman-Ford, A*, and Floyd-Warshall algorithms.
Shortest Path Algorithms
Introduction
The shortest path problem seeks the minimum-cost path between points in a graph, where cost can represent distance, time, or any numerical metric. This problem underpins critical applications in navigation, computer networks, robotics, logistics, social network analysis, and many other fields.
Problem Definition
Given a weighted graph G = (V, E) and vertices s (source) and t (target), find the path from s to t with minimum total weight.
Types of Shortest Path Problems
- Single-Source Shortest Path: From one vertex to all others
- Single-Destination Shortest Path: From all vertices to one target
- Single-Pair Shortest Path: Between two specific vertices
- All-Pairs Shortest Path: Between every pair of vertices
Turn real business decisions into optimization models and solve them in Python with free, open-source tools.
- Every chapter goes from a business story to tested code
- Routing, scheduling, facility location, finance and more
- Free solvers only: HiGHS, CBC, SCIP and CP-SAT