Connectivity and Centrality in Dense Random Geometric Graphs

Abstract: Due to shorter range communication becoming more prevalent with the development of multiple-input, multiple-output antennas (MIMO) and millimeter wave communications, multi-hop, intra-cell communication is anticipated to play a major role in 5G. This is developed in this thesis. Our analysis involves a stochastic spatial network model called a random geometric graph, which we use to model a network of interconnected devices communicating wirelessly without any separate, pre-established infrastructure. [The remaining abstract is available in the front matter of this thesis.]