Minimum Node Degree and k-Connectivity of a Wireless Multihop Network in Bounded Area

In a homogeneous wireless multihop network, the transmission range of nodes is an essential design parameter that critically affects the global design of the network. This paper investigates the relationship between the transmission range and two fundamental characteristics of wireless multihop networks: minimum node degree and k-connectivity. Conventional analysis assumes boundless network deployment area, which suffers from undesired border effects in practical applications based on bounded areas. To circumvent the border effect, this paper provides new analysis to accurately assess the network characteristics, including the upper bound and lower bound of both the minimum node degree and the k-connectivity. The analytical expressions hold for any arbitrary two-dimensional deployment area, when the nodes are densely deployed in a large and regular area. Simulation results corroborate with the derived analytical expressions.