Abstract
Small-world phenomenon is an important property of many complex networks possessing small average shortest path lengths and high clustering coefficients. On the other side, wireless ad-hoc networks are highly clustered having large average shortest path length caused by the locality of their physical connections. Since the average shortest path length (number of hops) traversed by data packets has a tight interplay with the level of quality of service experienced in the network, efforts have recently focused on the creation of small-world property in wireless networks. In this study, the concept of small world is investigated in the context of wireless ad-hoc networks in a Rayleigh fading environment. In particular, we prove that the extension of few wireless links to farther located nodes (using the concept of rewiring) can reduce the average shortest path length to a decent extent, even in the presence of severe channel fading. Simulation results show that a reduction of up to 23.3% in clustering coefficient and up to 25.6% in average shortest path length can be achieved for a low-density network in the presence of fading.