The analytical model of the WSNs will behavior different including data collected of the number of child node in each cluster and the random probability with the value ps.
Subsequently, WSNs is established by using the algorithmically that generates a pseudo random number [20, 21] is defined as a parameter of a variable X.
Here are the important properties of a multi-hop WSNs based on Monte Carlo simulation of uniformly cluster-tree topology.
Corollary 1: The size of a multi-hop WSNs based on a Monte Carlo algorithm to establish cluster tree uniformly topology consists the hop count (H) and the number of node child in each cluster (N) is defined as Ntotal which the accumulative X of all variable.
Corollary 2: The expanding topology in symmetries size Ntotal