SPECIAL ISSUE FOR CATS 2009 On the Structure of Classes of Random Graphs

Abstract: Many different random graph constructions are used to model large real life graphs, i.e., graphs that describe the structure of real systems. Often it is not clear, however, how the strength of the different models compare to each other, e.g., when does it hold that a certain model class contains another. We are particularly interested in random graph models that arise via abstract geometric constructions, motivated by the fact that these graphs can model wireless communication networks. We set up a general framework to compare the strength of random graph models, and present some results about the equality, inequality and proper containment of certain model classes, as well as some open problems.