  The Steiner $k$-eccentricity of a vertex $v$ of a graph $G$ is the maximum
Steiner distance over all $k$-subsets of $V (G)$ which contain $v$. In this
note, we design a linear algorithm for computing the Steiner $3$-eccentricities
and the connective Steiner $3$-eccentricity index on a tree and thus improving
a quadratic algorithm presented in [G. Yu, X. Li, \emph{Connective Steiner
3-eccentricity index and network similarity measure}, Appl. Math. Comput. 386
(2020), 125446.]
