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Connectivity of inhomogeneous random K-out graphs. (arXiv:1810.09921v1 [math.CO])
来源于:arXiv
We investigate the connectivity of wireless sensor networks secured by the
heterogeneous random pairwise key predistribution scheme. In contrast to the
homogeneous scheme proposed by Chan et al., where each node is paired (offline)
with $K$ other nodes chosen uniformly at random; herein, each node is
classified as class-$1$ with probability $\mu$ or class-$2$ with probability
$1-\mu$, for $0<\mu<1$, independently. Then, each class-$1$ (respectively,
class-$2$) node is paired (offline) with $K_1$ (respectively, $K_2$) other
nodes selected uniformly at random. We consider the particular case when
$K_1=1$ and $K_2=K$. The heterogeneous random pairwise scheme induces an
inhomogeneous random K-out graph $\mathbb{H} (n;\mu,K_n)$, where $n$ denotes
the number of nodes and $K_n$ denotes a scaling of $K$ with respect to the
network size $n$. Hence, establishing the connectivity of wireless sensor
networks secured by the heterogeneous random pairwise scheme maps to deriving
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