Connectivity and Structure in Large Networks

Abstract

Graph models play a central role in the description of real life complex networks. They aim at constructing graphs that describe the structure of real systems. The resulting graphs, in most cases, are random or random-like; so it is not surprising that there is a large literature on various classes of random graphs and networks. Our key motivating observation is that often it is unclear how the strength of the different models compare to each other, e.g., when will a certain model class contain another. We are particularly interested in random graph models that arise via (generalized) geometric constructions. This is motivated by the fact that these graphs can well capture wireless communication networks. We set up a general framework to compare the strength of random network models, and present some results about the equality, inequality and proper containment of certain model classes.