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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.

SUBMITTER: Stumpf MP

PROVIDER: S-EPMC555505 | biostudies-literature | 2005 Mar

REPOSITORIES: biostudies-literature

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Subnets of scale-free networks are not scale-free: sampling properties of networks.

Stumpf Michael P H MP Wiuf Carsten C May Robert M RM

Proceedings of the National Academy of Sciences of the United States of America 20050314 12

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 netwo ...[more]

PMID: 15767579

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Project description:BackgroundMany complex random networks have been found to be scale-free. Existing literature on scale-free networks has rarely considered potential false positive and false negative links in the observed networks, especially in biological networks inferred from high-throughput experiments. Therefore, it is important to study the impact of these measurement errors on the topology of the observed networks.ResultsThis article addresses the impact of erroneous links on network topological inference and explores possible error mechanisms for scale-free networks with an emphasis on Saccharomyces cerevisiae protein interaction networks. We study this issue by both theoretical derivations and simulations. We show that the ignorance of erroneous links in network analysis may lead to biased estimates of the scale parameter and recommend robust estimators in such scenarios. Possible error mechanisms of yeast protein interaction networks are explored by comparisons between real data and simulated data.ConclusionOur studies show that, in the presence of erroneous links, the connectivity distribution of scale-free networks is still scale-free for the middle range connectivities, but can be greatly distorted for low and high connecitivities. It is more appropriate to use robust estimators such as the least trimmed mean squares estimator to estimate the scale parameter gamma under such circumstances. Moreover, we show by simulation studies that the scale-free property is robust to some error mechanisms but untenable to others. The simulation results also suggest that different error mechanisms may be operating in the yeast protein interaction networks produced from different data sources. In the MIPS gold standard protein interaction data, there appears to be a high rate of false negative links, and the false negative and false positive rates are more or less constant across proteins with different connectivities. However, the error mechanism of yeast two-hybrid data may be very different, where the overall false negative rate is low and the false negative rates tend to be higher for links involving proteins with more interacting partners.

Dataset Information

Subnets of scale-free networks are not scale-free: sampling properties of networks.

Publications

Subnets of scale-free networks are not scale-free: sampling properties of networks.

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