Construction of scale-free networks with partial information

Abstract

It has recently been observed that the node degrees of many real-world large-scale networks, such as the Internet and the Web, follow a power law distributions. Since the classical random graph models are inadequate for explaining this phenomenon, alternative models have been proposed. However, most of the existing models unrealistically assume that each new joining node knows about all the existing nodes in the network. We relax this assumption and propose a model in which each new joining node uniformly and randomly chooses a sample set of existing nodes, and then connects to some nodes in the sample set according to the Preferential Attachment rule. We show that the power law of degree distribution still holds true even if each new joining node knows only a logarithmic number of existing nodes. Compared with the existing models, our construction of scale-free networks based on partial information seems to better approximate the evolution of certain complex networks arising in the real world. Our results may also be applied to the constructions of large-scale distributed systems such as peer-to-peer networks, where the global information is generally unavailable for any individual node in the network. © Springer-Verlag Berlin Heidelberg 2005.