Subnets of scale-free networks are not scale-free: Sampling properties of networks

Abstract

Most studies of networks have only looked at small subsets of the true network. Here, we discuss the sampling properties of a network's degree distribution under the most parsimonious sampling scheme. Only if the degree distributions of the network and randomly sampled subnets belong to the same family of probability distributions is it possible to extrapolate from subnet data to properties of the global network. We show that this condition is indeed satisfied for some important classes of networks, notably classical random graphs and exponential random graphs. For scale-free degree distributions, however, this is not the case. Thus, inferences about the scale-free nature of a network may have to be treated with some caution. The work presented here has important implications for the analysis of molecular networks as well as for graph theory and the theory of networks in general.complex networks ͉ protein interaction networks ͉ random graphs ͉ sampling theory

A Preliminary Study on the Effects of Fear Factors in Disease Propagation

“…Similar conclusion has been drawn on random node sampling in [17]. Therefore disease propagation in the sampled subnet reveals some different features from those in the original networks, as we shall discuss below.…”

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