This calculator helps you transform graph data into adjacency lists, a key representation in graph theory used by educators, students, and researchers.
Results
Data Source and Methodology
The adjacency list representation is based on standard graph theory concepts as detailed in VisuAlgo. All calculations are strictly based on the formulas and data provided by this source.
The Formula Explained
The adjacency list for a graph is constructed by listing each vertex and its corresponding set of adjacent vertices. This representation is efficient for storing sparse graphs.
AdjacencyList(Vertex) = {List of adjacent vertices}
Glossary of Terms
- Vertex: A node in the graph.
- Edge: A connection between two vertices.
- Adjacency List: A list where each vertex stores a list of adjacent vertices.
Example: A Step-by-Step Guide
Given edges a-b, b-c, and c-a, the adjacency list is:
a: b, c
b: a, c
c: a, b
Frequently Asked Questions (FAQ)
What is an adjacency list?
An adjacency list is a collection of lists used to represent a finite graph. Each list describes the set of neighbors of a vertex in the graph.
Why use an adjacency list?
It's efficient for sparse graphs and requires less memory compared to adjacency matrices.
How does this calculator work?
Enter the graph edges in the specified format, and it will output the corresponding adjacency list.
Can this handle directed graphs?
Yes, the input can be adjusted to represent directed edges.
What is the maximum number of vertices?
The calculator is optimized for small to medium-sized graphs.