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Interactive Graph Theory Learning

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Master graph theory through interactive lessons

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Graph Theory Courses

Multiple comprehensive PDF courses covering different aspects of graph theory

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Multiple comprehensive graph theory courses will be available here

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Available Lessons

Shortest Path Algorithms

Intermediate
Key Concepts:
DijkstraBellman-FordA* Algorithm+6 more
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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.

40 minutes
Intermediate
0/7 sections
DijkstraBellman-FordA* AlgorithmFloyd-WarshallBFSJohnson's AlgorithmShortest PathWeighted GraphsNegative Cycles

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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

  1. Single-Source Shortest Path: From one vertex to all others
  2. Single-Destination Shortest Path: From all vertices to one target
  3. Single-Pair Shortest Path: Between two specific vertices
  4. All-Pairs Shortest Path: Between every pair of vertices
Section 1 of 7