Graph Counting

Graph counting involves enumerating the number of possible graphs with given vertices (nodes) and edges.

Graph Basics

For a complete graph with \(n\) vertices, the number of edges is:

\[ E = \frac{n(n-1)}{2} \]

Example

How many edges in a complete graph with 4 vertices?

\[ E = \frac{4 \cdot 3}{2} = 6 \]

Applications

Graph counting is used in network design (e.g., internet topology), chemistry (e.g., molecular structures), and social network analysis.