Coupling Online and Offline Analyses for Random Power Law Graphs

We develop a coupling technique for analyzing online models by using offline models. This method is especially effective for a growth-deletion model that generalizes and includes the preferential attachment model for generating large complex networks which simulate numerous realistic networks. By coupling the online model with the offline model for random power law graphs, we derive strong bounds for a number of graph properties including diameter, average distances, connected components, and spectral bounds. For example, we prove that a power law graph generated by the growth-deletion model almost surely has diameter O(logn) and average distance O(log logn).