  The connective eccentricity index (CEI) of a graph $G$ is defined as
$\xi^{ce}(G)=\sum_{v \in V(G)}\frac{d_G(v)}{\varepsilon_G(v)}$, where $d_G(v)$
is the degree of $v$ and $\varepsilon_G(v)$ is the eccentricity of $v$. In this
paper, we characterize the unique graphs with maximum CEI from three classes of
graphs: the $n$-vertex graphs with fixed connectivity and diameter, the
$n$-vertex graphs with fixed connectivity and independence number, and the
$n$-vertex graphs with fixed connectivity and minimum degree.
