Calculate the number of edges in a complete graph
How to Use the Calculator
Follow these simple steps to calculate the number of edges:
- Enter the number of vertices (n) in the input field below.
- Click the “Calculate” button.
- The result will display the total number of edges in the complete graph.
- Check out the graphical representation of the complete graph drawn below.
A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. This means that every vertex is directly connected to every other vertex.
The formula to calculate the number of edges (E) in a complete graph with n vertices is:
E = n × (n – 1) / 2
This formula comes from the fact that each of the n vertices connects to n – 1 other vertices, and since each edge connects two vertices, we divide by 2 to avoid double-counting.
Applications
Complete graphs are fundamental in graph theory and have applications in network design, combinatorics, and computer science. Understanding the properties of complete graphs can help in solving problems related to networking, scheduling, and optimization.
Learn More
For more information on graph theory and complete graphs, consider visiting the following resources:
