Graph Shortest Path (Dijkstra Step-By-Step)

Graph Shortest Path (Dijkstra Step-By-Step) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: textarea, text, checkbox, number
Output type: text
Sample coverage: 4
API ready: Yes

Overview

The Graph Shortest Path tool computes the optimal route between nodes using Dijkstra's algorithm and provides a complete step-by-step trace of every iteration. It logs settled nodes, edge relaxations, distance updates, and the final reconstructed path for both directed and undirected weighted graphs.

When to use

Verifying manual Dijkstra calculations and distance tables for discrete mathematics or algorithm homework.
Tracing step-by-step edge relaxation behavior to understand why a greedy route fails in complex networks.
Finding the exact shortest distance and path between two vertices in weighted directed or undirected graphs.

How it works

1Enter graph edges one per line as source, destination, and non-negative weight (e.g., 'A B 4').
2Specify the source and target node identifiers, and choose whether edges should be treated as directed.
3The tool initializes distances, greedily settles the node with the minimum tentative distance, and relaxes outgoing edges.
4View the generated per-iteration log, settled distance states, and the final shortest path reconstruction.

Use cases

Computer science students checking homework traces and edge relaxation steps for Dijkstra exam problems.
Network engineers evaluating minimum latency or hop costs across simple routed network topologies.
Instructors generating step-by-step textbook-style pathfinding traces for discrete math lectures.

Examples

1. Undirected Six-Node Network Pathfinding

Computer Science Student

Background

Studying Dijkstra's algorithm in an algorithms course and solving manual trace assignments.

Problem

Needs to find the shortest path from node A to node F in an undirected graph and verify each relaxation step.

How to use

Paste the edge list into the edges textarea, set source to A, target to F, and leave directed unchecked.

Edges: A B 4, A C 2, B C 5, B D 10, C E 3, D E 4, D F 11, E F 8 | Source: A | Target: F | Directed: false

Outcome

Returns the complete step-by-step trace settling nodes in order and confirms the shortest path is A → C → E → F with a total distance of 13.

2. Directed Network Route Optimization

Network Administrator

Background

Evaluating transit costs and link metrics across a small directed routing topology.

Problem

Determine if a multi-hop path from node S to C offers lower latency than direct or alternate links.

How to use

Input the directed link costs, set the source to S, target to C, and enable the directed edges option.

FAQ

Can this tool handle graphs with negative edge weights?

No. Dijkstra's algorithm requires non-negative edge weights; negative values are rejected.

How are ties broken when multiple nodes have the same tentative distance?

Ties are resolved deterministically using the lexicographically smallest node identifier.

What happens if the target node is unreachable from the source?

The execution log traces all reachable settled nodes and reports the target as unreachable.

Does the tool support directed graphs?

Yes. Enable the 'Treat edges as directed' checkbox to ensure edges only travel from source to destination.

Can I use decimal numbers for edge weights?

Yes. Decimal weights are supported, and the decimal precision of the output can be customized.

Edges: S A 2, S B 4, A B 1, A C 7, B C 3 | Source: S | Target: C | Directed: true

Run this tool

Examples that match this tool

Continue with connected tools and hubs

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Undirected Six-Node Network Pathfinding

2. Directed Network Route Optimization

FAQ

Path Analyzer Samples

Import Path Examples

ELK Stack Log Analysis Samples

Copyright-Free MP3 Audio Samples

Audio to Text Transcriber (AI)

Indented List to ASCII Tree

Upside-Down Text

Assignment Problem Solver (Hungarian Algorithm)