Message Propagation Through Random Communication Networks

This study considers the message propagation problem in a "net-alert" situation through directed and undirected random networks having
n
nodes and probability of connection between the distinct pairs of nodes equal to
p
. The solution has been obtained by analyzing the structure of the random networks in terms of the probability distribution of the number of contacted new nodes, which are separated from the originator(s) of the message by simple chain progressions of
k
links. From these probability distributions, the average message propagation, the weak connectivity, and the
k
th terminal reliability are obtained. To aid the computation of these quantities first-order difference equations that approximate the average message propagation, the weak connectivity, and the
k
th terminal reliability are given. The application of the results is shown for random networks having several values of
n
and
p
.