Coupling Scale-Free and Classical Random Graphs

Abstract

Recently many new "scale-free'' random graph models have been introduced, motivated by the power-law degree sequences observed in many large-scale real-world networks. The most studied of these is the Barabási-Albert growth with "preferential attachment'' model, made precise as the LCD model by the present authors. Here we use coupling techniques to show that in certain ways the LCD model is not too far from a standard random graph; in particular, the fractions of vertices that must be retained under an optimal attack in order to keep a giant component are within a constant factor for the scale-free and classical models.