arXiv:2610.35970v1 Announce Type: new Abstract: The average eccentricity $\avec(D)$ of a strong digraph $D$ is the mean eccentricity of all vertices in $D$. A tournament $T$ is an orientation of a complete graph. In this paper, we prove that the average eccentricity satisfies $2 \le \avec(T) < \frac{n}{2k} + \frac{11}{2} + \frac{k}{8n}$ for a $k$-connected tournament $T$ of order $n$. We further examine the case for strong tournaments where $k = 1$, and show that $\avec(T) \le \frac{n+11}{2} + \frac{1}{8n}$ for any strong tournament $T$. Moreover, we show that the lower bound $2$ is sharp and that the upper bounds are best possible apart from an additive constant.
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