Graph approximations of spatial wireless network models

Wireless networks are usually modeled as spatial objects, and more specifically with random processes generating the locations of individual nodes. This is in stark contrast to the fixed networks case, in which graph models are typically used. While expressive, spatial models are usually more difficult to analyze than graph based ones, which has resulted in adoption of oversimplified models in wireless networks research. In this paper we show how wireless networks can be modeled as graphs without losing the accuracy of spatial models. We argue based on measurements of wireless network performance that in a number of cases distance-dependent interactions between wireless nodes can be discretized with only small approximation error. This discretization immediately yields an approximation of a spatial wireless network model as a graph with multiple edge types. We study the structure of the arising graph models, and show that the choice of accurate underlying spatial model remains important. For accurate spatial models, the corresponding graph approximations have a relatively simple neighborhood structure, indicating that they can be used very effectively in performance evaluation and optimization applications.