eccentricity

Eccentricity

The eccentricity of a vertex $v$ is the maximum shortest distance from $v$ to any other vertex in the graph.
Formally, if $d(v,u)$ denotes the shortest distance between vertices $v$ and $u$, then the eccentricity $\sigma (v)$ of vertex $v$ is defined as:

$$\sigma (v)=\underset{u\in V}{\max }d(v,u)$$

It helps quantify the importance of a vertex within the graph structure.
Outsiders have high eccentricity, while central nodes have low eccentricity.