A vertex is a point in a graph, an edge is a connection between two vertices, and the degree of a vertex is the number of edges incident to that vertex. A loop is counted twice when calculating degree.
The Key Definitions
This is part of AHL 3.14 Graph theory, so it is Mathematics: Applications and Interpretation HL-only content. A graph models relationships within a network, such as cities connected by roads or users connected on a social platform.
| Term | Meaning | Example |
|---|---|---|
| Vertex | A point representing an object or location | A city in a transport network |
| Edge | A line connecting two vertices | A road joining two cities |
| Degree | The number of edge-ends incident to a vertex | Three roads meeting at a city give degree three |
Consider an undirected graph with vertices (A, B, C, D) and edges (AB, AC, BC, CD). Its degrees are:
- , from and