Vertex eccentricity ecc(v) = max d(v,u): farthest distance from v. The eccentricity sequence lists all ecc values. max ecc = diameter, min ecc = radius. Peripheral: ecc=diam. Central: ecc=rad.
How to Use
Select graph:
- ecc(v): Per vertex
- Classes: Central/peripheral
- Sequence: All values
Vertex Classification
Central vertex: ecc(v)=rad(G). Peripheral vertex: ecc(v)=diam(G). In a path P_n: endpoints are peripheral (ecc=n-1), middle is central (ecc=⌈(n-1)/2⌉).
Properties
For any edge uv: |ecc(u)-ecc(v)|≤1. Eccentricity is a 1-Lipschitz function on the vertex set. The eccentricity sequence determines diam, rad, center, and periphery.
Step-by-Step Instructions
- 1Select graph.
- 2Compute all ecc(v).
- 3Find central vertices.
- 4Find peripheral vertices.
- 5Get diam and rad.