Acyclic Graph Data Structure Visualizer

Graph Visualization

Operation Steps

How to Use

Add Node: Enter a label and click "Add Node"
Add Edge: Enter source and destination, click "Add Edge"
Random Acyclic Graph: Click Random Acyclic Graph to instantly generate a sample DAG with random nodes and edges.
Remove Node/Edge: Select and remove as needed
Topological Sort: Click to see a valid ordering
Check Cycle: Click to check if the graph is acyclic
Reset: Click to clear the graph

Acyclic Graph Concept

Acyclic Graph is a directed graph with no cycles (DAG). It is widely used in scheduling, dependency resolution, and more.

Key Characteristics:

Directed edges
No cycles (no path from a node back to itself)
Supports topological ordering
Efficient for representing dependencies

Directed Graph: A graph where each edge has a direction, going from one node (the source) to another node (the target). In a directed graph, the edge (A → B) is not the same as (B → A). This allows us to represent dependencies and flows.

Topological Sort: An ordering of the nodes in a directed acyclic graph (DAG) such that for every directed edge (U → V), node U comes before node V in the ordering. Topological sort is useful for scheduling tasks, resolving dependencies, and more. Only possible if the graph has no cycles.

Purpose & Applications

Task scheduling
Build systems (dependency graphs)
Course prerequisite planning
Data processing pipelines
Version control (Git commit history)

Strengths & Limitations

Strengths:

Represents dependencies efficiently
Supports topological ordering
Cycle detection
Widely used in real-world applications

Limitations:

No cycles allowed
Not suitable for undirected or cyclic relationships
Visualization can be complex for large graphs

Time & Space Complexity

Operation	Time Complexity	Space Complexity
Add Node	O(1)	O(1)
Add Edge	O(1)	O(1)
Remove Node	O(V+E)	O(1)
Remove Edge	O(1)	O(1)
Topological Sort	O(V+E)	O(V+E)
Cycle Check	O(V+E)	O(V+E)