Analysis of k-Neigh Topology Control Protocol for Wireless Networks

k-Neigh is a basic neighbor-based topology control protocol based on the construction of k-neighbor graph as logical communication graph. Although k-neigh is based on a connectivity theory, several topological aspects of the constructed topology are not yet analytically investigated. In this paper, several topological properties of the constructed topology after execution of the protocol, including probability density function of the distance between each node to its ith neighbor, probability of unidirectional links after execution of the first phase of the protocol, average logical degree, and average final transmission range, are investigated analytically. Moreover, an extensive simulation study is performed to validate the analytical results.