Eccentricity of vertices in a graph when eccentricity of one vertex is given I have a very basic doubt. If a vertex in any graph has the eccentricity two, then what can be concluded about eccentricities of other vertices in graph. Is the eccentricity of every vertex is less than or equal to two? Can there exists any vertex whose eccentricity is greater than two. Kindly help. Just need a little hint for my problem. Thanks for giving time.

The eccentricity of every other vertex can be $4$, as looking at a path of length $5$ will tell you (there, the third element has eccentricity of $2$, while the edges have an eccentricity of $4$).

Can you show that the eccentricity cannot be more than $4$?