Eccentricity

Topics: Graph Theory

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In a connected graph, the eccentricity of a vertex $v_i$ is the length between $v_i$ and the farthest $v_j$.

That is:

$$E(v_i)=\max \{d(v_i,v_j)\mid v_i,v_j\in G\}$$

Centre of a Tree §

The concept of eccentricity is useful when we’re trying to identify the centre of a tree $c$, since:

$$E(c)=\min \{E(v_i)\}$$