Weighted Graph Visualizer

Create weighted graphs and inspect costs, paths, and structure through animated interactions, responsive controls, and clear explanations.

Editor ready

Weighted network laboratory

Weighted Graph Visualizer

Edit costs directly on the network and compare shortest-path relaxation with minimum-spanning-tree growth.

Algorithm console

Click nodes to assign endpoints; click an edge to edit its weight.

Editor ready

Algorithm

StartTarget

Playback

Step delayBalanced

Edge weight

No edge selected

Select an edge in the canvas to edit its cost.

Nodes

Edges

Visited

Step

0/0

Target distance

Select an algorithm and run the simulation.

Weighted network

Dijkstra workspace

start Atarget E

Legend

Start Node

End Node

Processing

Shortest Path

MST Edge

Live analysis

Dijkstra

Status

Ready / Paused

Shortest Distance

From A to E

Nodes Visited

0 / 5

About Dijkstra

Dijkstra's algorithm finds the shortest path between nodes in a graph. It picks the unvisited node with the smallest distance, calculates the distance through it to each unvisited neighbor, and updates the neighbor's distance if smaller.

Understanding Weighted Graphs

A Weighted Graph is a graph in which a number (the weight) is assigned to each edge. Such weights might represent costs, lengths or capacities, depending on the problem at hand. They are heavily used in GPS navigation systems, network routing, and resource allocation problems.

Dijkstra vs. Bellman-Ford

Dijkstra: Faster (O(E + V log V)), but fails with negative edge weights.
Bellman-Ford: Slower (O(VE)), but handles negative weights and detects negative cycles.

Weighted Graph Complete Info Card

Edge WeightsCost Optimization

A Weighted Graph is a graph structure where edges have associated numerical values (weights). Used to model real-world scenarios with costs, distances, capacities, or any quantifiable relationships. Enables sophisticated algorithms for path optimization and resource allocation.

Algorithm Complexities

Shortest Path (Dijkstra)

With priority queue

O(E log V)

Shortest Path (Bellman-Ford)

Handles negative weights

O(VE)

Minimum Spanning Tree

Prim's or Kruskal's

O(E log V)

Space Complexity

Adjacency list storage

O(V + E)

All Pairs Shortest Path

Floyd-Warshall

O(V³)

Negative Cycle Detection

Bellman-Ford

O(VE)

Graph Representations

Adjacency List with Weights

✓ Space efficient, flexible✗ Slower edge weight lookup

Adjacency Matrix with Weights

✓ O(1) weight access✗ O(V²) space

Edge List

✓ Simple, good for Kruskal's✗ Inefficient for traversal

Incidence Matrix

✓ Good for multi-graphs✗ Large memory footprint

Key Algorithms

Algorithm	Complexity	Primary Use Case	Key Features
Dijkstra's Algorithm	O(E log V)	Non-negative weights	Greedy, optimal for positive weights
Bellman-Ford	O(VE)	Handles negative weights	Detects negative cycles
Prim's Algorithm	O(E log V)	Minimum Spanning Tree	Greedy, grows from start node
Kruskal's Algorithm	O(E log V)	Minimum Spanning Tree	Union-Find, processes edges
Floyd-Warshall	O(V³)	All pairs shortest path	Dynamic programming approach

Weight Types & Applications

Positive Weights

Examples: Distances, costs, time

Algorithms: Dijkstra, Prim, Kruskal

Negative Weights

Examples: Profit/loss, energy flow

Algorithms: Bellman-Ford

Zero Weights

Examples: Free connections, neutral

Algorithms: All algorithms

Mixed Weights

Examples: Real-world networks

Algorithms: Bellman-Ford with care

Real-World Applications

Network Routing

Internet packet routing

Algorithm: Dijkstra's

Transportation

GPS navigation systems

Algorithm: A* (enhanced Dijkstra)

Social Networks

Influence propagation

Algorithm: Betweenness centrality

Circuit Design

Wire length minimization

Algorithm: Minimum Spanning Tree

Financial Networks

Arbitrage opportunities

Algorithm: Bellman-Ford

Optimal Use Cases

•Route planning and navigation systems
•Network design and infrastructure planning
•Resource allocation and cost optimization
•Supply chain and logistics management
•Social network analysis with influence metrics

Challenges & Considerations

•Negative weight cycles breaking algorithms
•Floating-point precision for real weights
•Dynamic weight updates requiring re-computation
•Memory overhead for storing weights
•Algorithm selection based on weight properties

Pro Tip: Use Dijkstra's algorithm for non-negative weights and Bellman-Ford when negative weights might be present. For minimum spanning trees, Prim's algorithm works better on dense graphs while Kruskal's excels on sparse graphs.

Path OptimizationCost AnalysisReal-world Modeling