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
Stump et al. show that the degree distributions of randomly sampled subnets of scale-free networks are not scale-free REF ; thus, subnet data cannot be naïvely extrapolated to every property of the entire network.
Subnets of scale-free networks are not scale-free: Sampling properties of networks
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Computer Science Medicine