Topology Characterization for Position-based Wireless Network Topology Generators

Topologies are usually characterized in terms of their network graph; usually by investigating their degree frequency, rank/degree, or hop/count distributions. Wireless network simulation, on the other hand, typically does not use network graphs. Instead, in most wireless simulations, nodes are first positioned on the terrain based on some positioning algorithm and then a radio propagation model is used to determine connectivity dynamically at simulation run-time. For this use-case, methods to characterize network topology based solely on the spacial positions of the nodes on the terrain are necessary. We propose several metrics and show how they can be used to evaluate position-based topologies: the nearest neighbor distance distribution, a threshold and a probabilistic node degree measure, and the application of an inhomogeneity measure for spatial distributions.