Non-searchability of random power-law graphs

Abstract

We investigate the complexity of searching for a given vertex in a scale-free graph, using only locally gathered information. In such graphs, the number of nodes of degree x is proportional to x-β for some constant β > 0. We consider two random scale-free graph models: the Chung-Lu model and the Móri model (a generalization of the Barabási-Albert model) proving two lower bounds of Ω(n log ⊖(β) n) and Ω(n1/2) on the expected time to find the worst-case target, under a restrictive model of local information. © Springer-Verlag Berlin Heidelberg 2007.