  In this paper, we consider a random network such that there could be a link
between any two nodes in the network with a certain probability (plink).
Diffusion is the phenomenon of spreading information throughout the network,
starting from one or more initial set of nodes (called the early adopters).
Information spreads along the links with a certain probability (pdiff).
Diffusion happens in rounds with the first round involving the early adopters.
The nodes that receive the information for the first time are said to be
covered and become candidates for diffusion in the subsequent round. Diffusion
continues until all the nodes in the network have received the information
(successful diffusion) or there are no more candidate nodes to spread the
information but one or more nodes are yet to receive the information (diffusion
failure). On the basis of exhaustive simulations conducted in this paper, we
observe that for a given plink and pdiff values, the fraction of successful
diffusion attempts does not appreciably change with increase in the number of
early adopters; whereas, the average number of rounds per successful diffusion
attempt decreases with increase in the number of early adopters. The invariant
nature of the fraction of successful diffusion attempts with increase in the
number of early adopters for a random network (for fixed plink and pdiff
values) is an interesting and noteworthy observation (for further research) and
it has not been hitherto reported in the literature.
