  Let $G_n$ be an $n$-dimensional recursive network. The $h$-embedded
connectivity $\zeta_h(G_n)$ (resp. edge-connectivity $\eta_h(G_n)$) of $G_n$ is
the minimum number of vertices (resp. edges) whose removal results in
disconnected and each vertex is contained in an $h$-dimensional subnetwork
$G_h$. This paper determines $\zeta_h$ and $\eta_h$ for the hypercube $Q_n$ and
the star graph $S_n$, and $\eta_3$ for the bubble-sort network $B_n$.
