Node Connectivity Analysis in Multi-Hop Wireless Networks

In this paper, we study node connectivity in multi-hop wireless networks. Nodal degree of connectivity as one of the fundamental graph properties is the basis for the study of network connectivity and has been a major research issue in multi-hop wireless networks. We use Random Geometric Graphs (RGG) to model multi-hop wireless networks and present a non-asymptotic analysis assuming bounded area and finite number of nodes. We assume random uniformly scattered nodes in a square-shaped bounded area. We derive a closed-form formula for the expected value of node degree of connectivity and propose an approximation algorithm for degree distribution in multi-hop wireless networks. Our extensive simulation results confirm that the proposed non-asymptotic analyses are quite accurate.