Graph Visualizer

Create nodes and edges, switch graph modes, and explore traversal behavior with responsive animations, controls, and graph insights.

Editor ready

Interactive graph laboratory

Graph Visualizer

Build a directed or undirected network, rearrange it freely, and watch BFS or DFS expose its traversal tree.

Graph console

Click two nodes to connect them; right-click a node or edge to delete it.

Editor ready

New node

Connect nodes

→

Traverse

Traversal speedBalanced

6 nodes6 edgesdirected0 visited

Graph workspace

Build and explore

activefrontierprocessed

Active

In Queue

Visited

Unreachable

Tree Edge

V = 6 · E = 6

What is a Graph?

A Graph is a non-linear data structure consisting of a finite set of Vertices (Nodes) and a set of Edges that connect these vertices. Graphs are used to model pairwise relations between objects, such as social networks, computer networks, and maps.

Time Complexity

Adjacency Matrix (Search)O(1)
Adjacency List (Search)O(V)
BFS TraversalO(V + E)
DFS TraversalO(V + E)

Key Concepts

✓
Directed vs UndirectedDirected graphs have edges with direction (one-way), while Undirected graphs have bidirectional edges (two-way).
✓
BFS vs DFSBFS explores neighbors layer by layer (Shortest Path). DFS explores as deep as possible before backtracking (Maze Solving).

Graph Complete Info Card

Non-linearNetwork

A Graph is a non-linear data structure consisting of vertices (nodes) and edges (connections). Used to represent networks, relationships, and dependencies. Essential for modeling real-world systems like social networks, transportation systems, and web pages.

Graph Characteristics

Space Complexity

Vertices + Edges storage

O(V + E)

BFS/DFS Time

Visit all vertices and edges

O(V + E)

Shortest Path (Dijkstra)

With priority queue

O(E log V)

Cycle Detection

Using DFS

O(V + E)

Connectivity

Using BFS/DFS

O(V + E)

Topological Sort

For DAGs

O(V + E)

Graph Representations

Adjacency Matrix

✓ O(1) edge lookup✗ O(V²) space

Adjacency List

✓ O(V + E) space✗ O(degree) edge lookup

Edge List

✓ Simple implementation✗ Inefficient queries

Incidence Matrix

✓ Good for multi-graphs✗ Large memory footprint

Common Graph Algorithms

Category	Algorithms	Primary Use Case
Traversal	BFS, DFS	Explore graph structure
Shortest Path	Dijkstra, Bellman-Ford, Floyd-Warshall	Find optimal routes
Minimum Spanning Tree	Prim, Kruskal	Connect all nodes minimally
Cycle Detection	DFS, Union-Find	Find cycles in graph
Topological Sort	Kahn's, DFS-based	Order dependencies

Graph Types & Examples

Directed

Edges have direction

Example: Web links, dependencies

Undirected

Edges are bidirectional

Example: Social networks, roads

Weighted

Edges have weights

Example: Maps with distances

Unweighted

All edges equal

Example: Social connections

Cyclic

Contains cycles

Example: Most real networks

Acyclic

No cycles (DAG)

Example: Task dependencies

Graph Properties

•Degree: Number of edges connected to a vertex
•Path: Sequence of vertices connected by edges
•Cycle: Path that starts and ends at same vertex
•Connectivity: Whether all vertices are reachable
•Density: Ratio of actual edges to possible edges

Optimal Use Cases

•Social network analysis
•Routing and navigation systems
•Dependency resolution
•Recommendation systems
•Web crawling and indexing

Challenges & Considerations

•Memory-intensive for large graphs
•Complex algorithm implementations
•Scalability with billions of edges
•Choosing appropriate representation
•Dynamic graph updates

Pro Tip: Use adjacency lists for sparse graphs and adjacency matrices for dense graphs. For very large graphs, consider distributed graph databases or specialized graph processing frameworks.

Network ModelingPath FindingRelationship Analysis