  Random graphs are an important tool for modelling and analyzing the
underlying properties of complex real-world networks. In this paper, we study a
class of random graphs known as the inhomogeneous random K-out graphs which
were recently introduced to analyze heterogeneous sensor networks secured by
the pairwise scheme. In this model, first, each of the $n$ nodes is classified
as type-1 (respectively, type-2) with probability $0<\mu<1$ (respectively,
$1-\mu)$ independently from each other. Next, each type-1 (respectively,
type-2) node draws 1 arc towards a node (respectively, $K_n$ arcs towards $K_n$
distinct nodes) selected uniformly at random, and then the orientation of the
arcs is ignored. From the literature on homogeneous K-out graphs wherein all
nodes select $K_n$ neighbors (i.e., $\mu=0$), it is known that when $K_n
\geq2$, the graph is $K_n$-connected asymptotically almost surely (a.a.s.) as
$n$ gets large. In the inhomogeneous case (i.e., $\mu>0$), it was recently
established that achieving even 1-connectivity a.a.s. requires $K_n=\omega(1)$.
Here, we provide a comprehensive set of results to complement these existing
results. First, we establish a sharp zero-one law for $k$-connectivity, showing
that for the network to be $k$-connected a.a.s., we need to set $K_n =
\frac{1}{1-\mu}(\log n +(k-2)\log\log n + \omega(1))$ for all $k=2, 3, \ldots$.
Despite such large scaling of $K_n$ being required for $k$-connectivity, we
show that the trivial condition of $K_n \geq 2$ for all $n$ is sufficient to
ensure that inhomogeneous K-out graph has a connected component of size
$n-O(1)$ whp.
